LOGARITHMIC AND TRIGONOMETRIC TABLES A SERIES OF MATHEMATICAL TEXTS (FOR COLLEGES) EDITED BY EARLE RAYMOND HEDRICK THE CALCULUS BY ELLEBY WILLIAMS DAVIS and WILLIAM CHARLES BRENKE. ANALYTIC GEOMETRY AND ALGEBRA BY ALEXANDER ZIWET and Louis ALLEN HOPKINS. ELEMENTS OF ANALYTIC GEOMETRY BY ALEXANDER ZIWET and Louis ALLEN HOPKINS. PLANE AND SPHERICAL TRIGONOMETRY BY ALFRED MONROE KENYON and Louis INGOLD. ELEMENTARY MATHEMATICAL ANALYSIS BY JOHN WESLEY YOUNG and FRANK MILLETT MORGAN. PLANE TRIGONOMETRY BY JOHN WESLEY YOUNG and FRANK MILLETT MORGAN. COLLEGE ALGEBRA BY ERNEST BROWN SKINNER. MATHEMATICS FOR AGRICULTURE AND GENERAL SCIENCE BY ALFRED MONROE KENYON and WILLIAM VERNON LOVTTT. MATHEMATICS FOR STUDENTS OF AGRICULTURE BY SAMUEL EUGENE RASOR. THE MACMILLAN TABLES Prepared under the direction of EARLE RAYMOND HEDBICK. A BRIEF COURSE IN COLLEGE ALGEBRA BY WALTER BURTON FORD. COLLEGE ALGEBRA BY ARTHUR M. HARDING and GEORGE W. MULLINS. PLANE TRIGONOMETRY BY ARTHUR M. HARDING and GEORGE W. MULLINS. GENERAL MATHEMATICS BY CLINTON H. CURRIER and EMERY E. WATSON. PROJECTIVE PURE GEOMETRY BY THOMAS F. HOLGATE ANALYTIC GEOMETRY BY ARTHUR M. HARDING and GEORGE W. MULLINS. INTRODUCTION TO HIGHER GEOMETRY BY WILLIAM C. GRAUSTEIN. INTRODUCTION TO TRIGONOMETRY AND ANALYTIC GEOMETRY BY ERNEST BROWN SKINNER. DIFFERENTIAL AND INTEGRAL CALCULUS BY JOHN HAVEN NEELLEY and JOSHUA IRVING TRACEY. THE MONGEAN METHOD OF DESCRIPTIVE GEOME- TRY BY WILLIAM HENRY ROEVER. DIFFERENTIAL EQUATIONS BY NELSON B. CONKWRIGHT. TABLES OF INTEGRALS AND OTHER MATHEMATICAL DATA BY HERBERT BRISTOL DWIGHT. AN INTRODUCTION TO THE MATHEMATICS OF LIFE INSURANCE BY WALTER O. MENGE and JAMES W. GLOVER. LOGAEITHMIC AND TRIGONOMETRIC TABLES REVISED EDITION PREPARED UNDER THE DIRECTION OF EARLE RAYMOND HEDRICK ENTIRELY RE-SET IN A NEW TYPE FACE NEW YORK THE MACMILLAN COMPANY COPYRIGHT, 1913 AND 1920, Br THE MACMILLAN COMPANY. All rights reserved no part of this book may be reproduced in any form without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages in connection with a review written for inclusion in magazine or newspaper. Set up and electrotyped. Revised edition published August, 1920. Reprinted April, 1924 ; May, September, December, 1925 ; April, June, 1926 ; January, July, 1927 ; March, December, 1928 ; November, 1929 ; October, November, 1930 ; April, October, 1931; February, 3932; April, 1933; May, 1933; November, 1933; July, 1935; May, 1936; December, 1937; May, 1938; June, 1938; December, 1939; August, 1940; October, 1940; May, 1941. Printed in the United States of America PREFACE The present edition of this book contains all of the tables in the previous editions. All have been reset in a new and very readable type. Great care has been exercised to preserve and to increase the great degree of reliability that existed in the previous edition. For careful reading of the proofs, I am indebted to my daughter Elisabeth and her husband, Mr. Richard L. Miller, to several of my own students, and to the following friends in other institutions, sometimes with the aid of their students : Professor C. H. Currier, Brown University ; Pro- fessor H. T. Davis, University of Indiana; Professor H. B. Dwight, Massachusetts Institute of Technology; Professor W. B. Ford, Uni- versity of Michigan ; Professor A. M. Harding, University of Arkansas ; Professor C. G. Jaeger, Pomona College ; Professors H. W. Kuhn and J. H. Weaver, Ohio State University; Professor L. S. Johnston, Uni- versity of Detroit; Professors A. J. Kempner and C. A. Hutchinson, University of Colorado; Professor G. W. Mullins, Barnard College (Columbia University) ; Professor L. M. Passano, Massachusetts Insti- tute of Technology; Professors H. L. Rietz, Roscoe Woods, and J. F. Reilly, University of Iowa; Professor E. E. Watson, Iowa State Teachers College at Cedar Falls; Dr. E. W. Wilson, Cambridge, Mass.; and Pro- fessor Kathryn Wyant, Athens College, Athens, Alabama. Each of these persons or groups has read the complete proof. With deep feeling, I may record also that the late Professor Louis Ingold of the University of Missouri read the proofs up to page 54, and had sent me the last of these pages within a week of his sudden death on January 25, 1935. These careful readings render the possibility of printers' errors ex- tremely remote. While the calculation of the probability that an undiscovered error exists is not simple, a strict account has been kept of each error found and of the total number not found by any one group of readers, so that a basis for a statistical calculation is known: the result- ing probability that even one undiscovered printers' error exists is not more than one in many thousands. I desire to express here my thanks to all those, particularly those mentioned above, who have assisted in the effort to make these tables so free from errors and therefore so reliable. I know of no comparable method for securing this quality in a set of tables. I repeat also my acknowledgment made in the original edition to many previously existing tables, particularly those of Vega and those of Hoiiel. During the proof-reading, those who have assisted have compared these tables with a great variety of existing tables, including several high-place tables, and the values have been recalculated and checked whenever a disagreement has been discovered. Finally, I wish to mention the excellent cooperation of the editorial staff of the Macmillan Company under the able direction of Mr. F. T. Sutphen. E. R. HEDRICK CONTENTS PAGES EXPLANATION OF THE TABLES vii-xvi TABLES PRINCIPALLY TO FIVE PLACES TABLE I. COMMON LOGARITHMS OP NUMBERS .... 1-19 TABLE la. CONDENSED LOGARITHMS AND ANTILOGARITHMS . . 20 TABLE II. ACTUAL VALUES OP THE TRIGONOMETRIC FUNCTIONS. 21-44 TABLE Ilia. VAIUES OP S AND T FOR INTERPOLATION ... 45 TABLE III. COMMON LOGARITHMS OF THE TRIGONOMETRIC FUNC- TIONS 45-90 REDUCTION OP DEGREES TO RADIANS .... 91 TRIGONOMETRIC FUNCTIONS OF ANGLES IN RADIAN'S . 92-93 REDUCTION OF RADIANS TO DEGREES .... 93 POWERS ROOTS RECIPROCALS 94-111 NAPIERIAN OR NATURAL LOGARITHMS .... 112-114 MULTIPLES OF M AND OF 1/M 115 VALUES AND LOGARITHMS OF HYPERBOLIC FUNCTIONS 116-122 VALUES AND LOGARITHMS OF HAVERSINES . . . 123-125 FACTOR TABLE LOGARITHMS OF PRIMES . . . 126-127 COMPOUND INTEREST 128 COMPOUND DISCOUNT 129 AMOUNT OF AN" ANNUITY 130 PRESENT VALUE OF AN ANNUITY 131 LOGARITHMS FOR INTEREST COMPUTATIONS . . . 132 AMERICAN EXPERIENCE MORTALITY TABLE . . . 132 IMPORTANT CONSTANTS . 133 IV. V. Va. VI. TABLE TABLE TABLE TABLE TABLE VII. TABLE VIII. TABLE IX. TABLE X. TABLE XL TABLE Xlla. TABLE XII6. TABLE XIIc. TABLE Xlld. TABLE Xlle. TABLE XII/. TABLE XIII. BRIEF TABLES PRINCIPALLY TO FOUR PLACES TABLE XlVa. COMMON LOGARITHMS 134-135 TABLE XlVb. ANTILOGARITHMS 136-137 TABLE XIVc. VALUES AND LOGARITHMS OF TRIGONOMETRIC FUNC- TIONS . 138-142 EXPLANATION OF THE TABLES TABLE I. FIVE-PLACE COMMON LOGARITHMS OF NUMBERS FROM 1 TO 10000 1. Common Logarithms. The power to which 10 must be raised to produce any number n is called the common logarithm * of n. Thus log 10 = 1, log 100 = 2, log 1000 = 3, etc.; log 1 = 0, log 0.1 = -1; log 0.01 = -2, log 0.001 = 3, etc. In general, if 10* = n, I is called the common logarithm of n, and is denoted by log n. 2. Fundamental Principles. Logarithms constitute a great labor-saving de- vice in arithmetical computations. The principles of their application are stated as follows: I. The logarithm of a -product is equal to the sum of the logarithms of the factors: log ab = log a + log 6. This follows from the fact that if 10' = a and itf 1 = 6, IQI+L = a- b. In brief: to multiply, add logarithms. II. The logarithm of a fraction is equal to the difference obtained by subtracting the logarithm of the denominator from the logarithm of the numerator: log (afb) = log a - log 6. For, if 10' = a and 10 L = 6, then 10'-^ = 0-7-6. In brief: to divide, subtract logarithms. III. The logarithm of a power is equal to the logarithm of the base multiplied by the exponent of the power: log a 6 = b log a. This follows from the fact that if 10' = a, then 10' 6 = a b . IV. The logarithm of a root of a number is found by dividing the logarithm of the number by the index of the root: log ^a = (log a)/6. This follows from the fact that if 10' = a, then 10" 6 = a 1 / 6 = \Ja. Corollary of II. The logarithm of the reciprocal of a number is the negative of the logarithm of the number: log (I/a) = log a, since log 1 = 0. 3. Characteristic and Mantissa. Every real positive number has a real common logarithm. If a and b are any two real positive numbers such that a 1. However, a much more rapid process depends on the use of Tables I and XI with this table. Thus, by Table I, 10 -* 3429 = 2.718, nearly. By Table XI, log 2.718 = 0.43424 94524 . Hence 10- 9 819 = (2.718) (10- OOOM 5029S ) = (2.718) (10 - 00004 )(10- 0000060298 ). Obtaining the second factor from this table, and the last factor from the formula 10* = 1 + (l/Af)z, by Table VIII, we find 10-*2 44819 = 2.71828 1828; the correct value is 2.718281828459 -. This process requires only two long multiplications. II. FIVE-PLACE TABLE OF THE ACTUAL VALUES OF THE TRIGONOMETRIC FUNCTIONS OF ANGLES 10. Direct Readings. This table gives the sines, cosines, tangents, and cotangents of the angles from to 45; and by a simple device, indicated by the printing, the values of these functions for angles from 45 to 90 may be read directly from the same table. For angles less than 45 read down the page, the degrees being found at the top and the minutes on the left; for angles greater than 45 read up the page, the degrees being found at the bottom and the minutes on the right. To find a function of an angle (such as 15 27'.6, for example) which does not reduce to an integral number ot minutes, we employ the process of inter- xii EXPLANATION OF THE TABLES [10 polation. To illustrate, let us find tan 15 27'.6. In the table we find tan 15 27' = 0.27638 and tan 15 28' = 0.27670; we know that tan 15 27'.6 lies between these two numbers. The process of interpolation depends on the assumption that between 15 27' and 15 28' the tangent of the angle varies directly as the angle; while this assumption is not strictly true, it gives an approximation sufficiently accurate for a five-place table. Thus we should assume that tan 15 27'.5 is halfway between 0.27638 and 0.27670. We may state the problem as follows: An increase of 1' in the angle increases the tangent 0.00032; assuming that the tangent varies as the angle, an increase of 0'.6 in the angle will increase the tangent by 0.6 X 0.00032 = 0.00019 (retaining only five places) ; hence tan 15 27'.6 = 0.27638 + 0.00019 = 0.27657. The difference between two successive values in the table is called, as in Table I, the tabular difference (0.00032 above). The proportional part of the tabular difference which is used is called the correction (0.00019 above), and is found by multiplying the tabular difference by the appropriate fraction of the smallest unit given in the table. Example 1. Find sin 63 52'. 8. We find sin 63 52' = 0.89777; tabular difference = 0.00013 (subtracted mentally from the table), correction = 0.8 X 0.00013 = 0.00010 (to be added). Hence sin 63 52'.8 = 0.89787. Example 2. Find cos 65 4 24'.8. cos 65 24' = 0.41628; tabular difference = 26; 0.8 X 26 =21 (to be subtracted because the cosine decreases as the angle increases). Hence cos 65 24'.8 = 0.41607. RULE. To find a trigonometric function of an angle by interpolation: select the angle in the table which is next smaller than the given angle, and read its sine (cosine or tangent or cotangent as the case may be) and the tabular difference. Compute the correction as the proper proportional part of the tabular difference. In case of sines or tangents add the correction; in case of cosines or cotangents, subtract it. 11. Reverse Readings. Interpolation is also used in finding the angle when one of its functions is given. Example 1. Given sin x 0.32845, to find x. Looking in the table we find the sine which is next less than the given sine to be .32832, and this belongs to 19 10'. Subtract the value of the sine selected from the given sine to obtain the actual difference = 0.00013; note that the tabular difference = 0.00027. The actual dif- ference divided by the tabular difference gives the correction = 13/27 = 0.5 as the decimal of a minute (to be added). Hence x = 19 10'. 5. Example 2. Given cos x = 0.28432, to find x. The cosine in the table next less than this is 0.28429 and belongs to 73 29'; the tabular dif- ference is 28; the actual difference is 3; correction = 3/28 =0.1 (to be subtracted). Hence x = 73 28' .9. RULE. To find an angle when one of its trigonometric functions is given: select from the table the same named function which is next less than the given function, noting the corresponding angle and the tabular difference; compute the actual difference (between~the selected value of the function and the given value) and divide 12] TRIGONOMETRIC FUNCTIONS xiii it by the tabular difference; this gives the correction which is to be added if the given function is sine or tangent, and to be subtracted if the given function is cosine or cotangent. III. FIVE-PLACE COMMON LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS 12. Use of the Table. If it is required to find the numerical value of x = 27.85 X sin 51 27', we may apply logarithms as follows: log 27.85 = 1.44483. log sin 51 27' = 9.89324 - 10 (add) log x = 1.33807 x = 21.78 The only new idea here is the method of finding log sin 51 27', which means the logarithm of the sine of 51 27'. The most obvious way is to find in Table II, sin 51 27' = 0.78206, and then to find in Table I, log 0.78206 = 9.89324 - 10, but this involves consulting two tables. To avoid the necessity of doing this, Table III gives the logarithms of the sines, cosines, tangents, and cotangents. The arrangement and the principles of interpolation are similar to those given on p. vii for Table I. The sines and cosines of all acute angles, the tangents of all acute angles less than 45 and the cotangents of all acute angles greater than 45 are proper fractions, and their logarithms end with 10, which is not printed in the table, but which should be written down whenever such a logarithm is used. In the printed table, values are stated so that 10 should be subtracted in every case. Example I. Find log sin 68 25'.4. On the page having 68 at the bottom, and in the row having 25' on the right find log sin 68 25' = 9.96843 10; the tabular difference is 5; 0.4 X 5 is given in the margin as 2; this is the correction to be added, giving log sin 68 25'.4 = 9.96845 10. (In case of sine and tangent add the correction. In case of cosine and cotangent, subtract the correction.) Example 2. Given log cos x = 9.72581 10, to find x. The logarithmic cosine next less than the given one is 9.72562 10 and belongs to 57 53'; the actual difference is 19; the tabular difference is 20; hence the correction is 19/20 = 1.0 (to the nearest tenth) ; (subtract) ; hence x = 57 52'.0. In finding log ctn a for any angle a, note that log ctn a = log tan a, since ctn a = I/tan a. Hence the tabular differences for log ctn are precisely the same as those for log tan throughout the table, but taken in reversed order. Likewise, log sec a. = log cos a, log esc a = log sin a; hence the values of log sec a. and log esc a are omitted. For angles near or near 90, the interpolations are not very accurate if the differences are large. For the calculation of sine or tangent near 0, Table Ilia, page 45, gives the values of S = log sin A log A' and T = log tan A log A', where A is the given angle and A' is the number of minutes in A, for values of A between and 3. Then log sin A = log A' + S and log tan A = log A' + T, for small angles. Moreover, since we have cos A = sin (90 A) and ctn A = tan (90 - A). xiv EXPLANATION OF THE TABLES [12 log cos A = log (90 -AY +8 and log ctn A = log (90 - A)' + T, when A is near 90. Another method practically equivalent to the preceding is to use the ap- proximate relations log sin A log sin B = log A' log B' and log tan A log tan B = log A' log B', vrhere A is the given angle and B is the nearest angle to A that is given in the table. If A < 3 and | A B \ < 1', these formulas give log sin A and log tan A to five decimal places. IV-V. RADIAN MEASURE 13. Computations in Radian Measure. The reduction of degrees to radians is facilitated by Table IV Conversion of Degrees to Radians. Since TT radians = 180, this table may be regarded as a table of multiples of ir/180. The values of sin x, cos x, tan x, are stated for every angle x from 0.00 to 1.60 radians at intervals of 0.01 radian in Table V Trigonometric Functions in Radian Measure. The values of any of these functions for larger values of x may be computed by first converting the value of the angle in radian measure to degree measure, by Table Va, and then finding the value of the function from Table II. The reduction of radians to degrees can be performed directly by Table V; or, for greater accuracy, by the supplementary Table Va. VI. POWERS ROOTS RECIPROCALS ty_ : \ uare, c 14. Arrangement. This table is arranged so that the square, cube, square , root, cube root, or reciprocal can be read directly to five decimal places for any number n of three significant figures. To attain this, not only n 2 , n 3 , Vw, \fn, 1/n, but also VlOn, -v'lOn, -v'lOOn are printed on every page. All values have been carefully recomputed and checked. Thus to find Vl.17, read in Vn column the result: 1.08167. To find Vll.7, read in the same line, in VlOn column the result: 3.42053. To find VTl7, read 10 times the entry in Vn column, since VTl7 = 10 VTl7. Similarly, -\J1.17 = 1.05373 from -^/n column; -y^ll.7 = 2.27019 from the same line in -\llOn column; -^117 = 4.89097 from the same line in VlOOn column. The effect of a change in the decimal point in n 2 , n 3 , and 1/n is only to shift the decimal point in the result, without altering the digits printed. VII. NAPIERIAN OR NATURAL LOGARITHMS 15. The Base e. Natural Logarithms. The number e = 2.7182818 is called the natural base of logarithms. The logarithms of numbers to this base are given in Table VII at intervals of 0.01 from 0.01 to 10.09, and at unit intervals from 10 to 409. The fundamental relation log n = log e 10 X logic n enables us to transfer from the base 10 to the base e, or conversely; where log. 10 = 2.30258509 -. 19] OTHER TABLES XV VIII. MULTIPLES OF M AND OF 1/M 16. Multiples of M and 1/M. This table is convenient whenever a number is to be multiplied by M or by 1/Af. This occurs whenever it is desired to change from common logarithms to natural logarithms, or conversely, since M = logio e and since we have log x = (log e 2) (logio ) = M log e x and log e x = (II M) log x. Other formulas that require these multiples are logio e* - x logic e = x- M and log e (10 n 'x) = log, x -f- n(l/Af); and the approximate formulas (see 8, 9, pp. x, xi) logio (1 x) = x-Af and 10** = 1 (l/Af)z. IX. VALUES AND LOGARITHMS OF HYPERBOLIC FUNCTIONS 17. Hyperbolic Functions. This table gives the values of e*, e~~*, sinh x, cosh x, tanh x; and the logarithms of e x , sinh x, cosh z, at varying intervals from x = to x = 10. It is to be noted that log e~ x = log e* and log tanh x = log sinh x log cosh x. The table may be extended indefinitely by means of Table VIII, since Iog 10 e* = x- M; for this reason Table VIII may be regarded as a table of values of logio e*. X. VALUES AND LOGARITHMS OF HAVERSINES 18. Haversines. This table gives the values and the logarithms of the haversines of angles from to 180 at intervals of 10'. The haversine, which means half of the versed sine, is hav A = (Yd vers A = (Y^)(l - cos A); hence its values to five places may be computed from the table of cosines. It is used extensively in navigation, and it may be used to advantage in the solution of ordinary oblique triangles. XI. FACTOR TABLE LOGARITHMS OF PRIMES 19. Factors of Composite Numbers. Logarithms of Primes. The uses of this table are evident in questions involving factoring, and for finding high- place logarithms of numbers whose prime factors are less than 2018. We shall illustrate the finding of logarithms of other numbers by finding log IT. Taking w = 3.14159 26536, divide by 3 (the first digit), obtaining 1.04719 75512 . Divide this quotient by 1.047 (in general, by the nearest first four digits), obtaining 1.00018 8683 . By Table VIII, the approxi- mate formula log (1 x) = X'M gives log 1.00018 8683 = 0.00008 1944 (Table VIII) log 3 = 0.47712 12547 (Table XI) log 1.047 = log 3 + log 0.349 = 0.01994 66817 (Table XI) log TT = 0.49714 9880 while the true value of log IT is 0.49714 98726 9, so that the error is less than 1 in the eighth place. In general, this process will give the logarithm of any number to within 6 in the eighth decimal place, and the probable error is less than 1.5 in the eighth place. For still greater accuracy, see Table la and 10. xvi EXPLANATION OF THE TABLES [20 XII. INTEREST TABLES 20. Interest Tables. Tables XII a, b, c, d give compound interest and annuity data for various per cents up to fifty years. Aside from the obvious uses, formulas involving these data will be found in works on statistics, ac- counting, and the mathematics of business. Table XHe gives the logarithms of (1 + r) to fifteen places, for all ordinary values of r from J^% to 10%. For other values of r, log (1 + r) may be computed from Table la (see 8). The final result in interest calculations may be obtained to nine significant figures by the antilogarithms of Table la (see 9). Table XII/ is the American Experience Mortality Table. XIV. FOUR-PLACE TABLES 21. Four-place Tables. These are duplicates of the preceding five-place tables, reduced to four places, and with larger intervals between the tabulations. The value of such four-place tables consists in the greater speed with which they can be used, in case the degree of accuracy they afford is sufficient for the purpose in hand. XIVo. Logarithms of Numbers. The only special feature of this table is that the proportional parts are printed for every tenth in every row; hence the logarithm of any number of four significant figures can be read directly. XIV6. Antilogarithms. This table will be found to facilitate approximate calculations to a marked degree. The proportional parts are stated in the right-hand margin for each row separately. This arrangement, with the corresponding one in Table XlVa, makes the tables effectively four-place each way. XIVc. Values and Logarithms of Trigonometric Functions. In this table, the values of sin a, cos a, tan a, ctn a, and their common logarithms, are stated for each 10-minute interval in a. The characteristics of the logarithms are omitted, since they can be supplied readily from the value. Greek Alphabet LETTERS NAMES LETTERS NAMES LETTERS NAMES LETTERS NAMES A a Alpha H n Eta N V Nu T r Tau B Beta e e Theta g % Xi T V Upsilon r 7 Gamma i t Iota Omicron * Phi A 5 Delta K K Kappa n IT Pi X X Chi E e Epsilon A X Lambda p P Rho * * Psi Z f Zeta M M Mu S o- s Sigma fl w Omega LOGARITHMIC AND TRIGONOMETRIC TABLES TABLE I COMMON LOGARITHMS OF NUMBERS FROM 1 TO 10 000 TO FIVE DECIMAL PLACES 1 100 N Log N Log N Log N Log N Log 20 1.30 103 40 1.60206 60 1.77815 80 1.90 309 1 2 3 0.00 000 0.30 103 0.47 712 21 22 23 1.32 222 1.34 242 1.36 173 41 42 43 1.61 278 1.62 325 1.63 347 61 62 63 1.78 533 1.79 239 1.79 934 81 82 83 1.90849 1.91 381 1.91 908 4 5 6 0.60 206 0.69 897 0.77 815 24 25 26 1.38 021 1.39 794 1.41 497 44 45 46 1.64 345 1.65 321 1.66276 64 65 66 1.80 618 1.81 291 1.81 954 84 85 86 1.92 428 1.92 942 1.93 450 7 8 9 0.84510 0.90 309 0.95 424 27 28 29 1.43 136 1.44716 1.46 240 47 48 49 1.67 210 1.68 124 1.69 020 67 68 69 1.82 607 1.83 251 1.83 885 87 88 89 1.93 952 1.94 448 1.94 939 10 1.00 000 30 1.47 712 50 1.69 897 70 1.84510 90 1.95424 11 12 13 1.04 139 1.07918 1.11 394 31 32 33 1.49 136 1.50515 1.51 851 51 52 53 1.70 757 1.71 600 1.72 428 71 72 73 1.85 126 1.85 733 1.86 332 91 92 93 1.95 904 1.96 379 1.96 848 14 15 16 1.14 613 1.17 609 1.20412 34 35 36 1.53 148 1.54 407 1.55 630 54 55 56 1.73 239 1.74 036 1.74 819 74 75 76 1.86 923 1.87 506 1.88 081 94 95 96 1.97 313 1.97 772 1.98227 17 18 19 1.23 045 1.25 527 1.27 875 37 38 39 1.56 820 1.57 978 1.59 106 57 58 59 1.75 587 1.76 343 1.77 085 77 78 79 1.88 649 1.89 209 1.89 763 97 98 99 1.98 677 1.99 123 1.99 564 N Log N Log N Log N Log N Log 2 100 Logarithms of Numbers 150 \ c; 1 = "^ N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 100 00000 043 087 130 173 217 260 303 346 389 101 432 475 518 561 604 647 689 732 775 817 44 43 48 102 860 903 945 988 *030 *072 *115 *157 *199 *242 1 4.4 4.3 4.2 103 01284 326 368 410 452 494 536 578 620 662 2 8.8 8.6 8.4 104 105 703 02119 745 160 787 202 828 243 870 284 912 325 953 366 025=. 30r ^036 "449" *078 490 3 4 13.2 17.6 12.9 17.2 12.6 16.8 106 531 572 612 653 694 735 776 816 857 898 5 6 22.0 26.4 21.5 25.8 21.0 25.2 107 938 979 *019 *060 *100 *141 *181 *222 *262 *302 7 30.8 30.1 29.4 108 03342 383 423 463 503 543 583 623 663 703 8 35.2 34.4 33.6 109 743 782 822 862 902 941 981 *021 *060 *100 9 39.6 38.7 37.8 110 04139 179 218 258 297 336 376 415 454 493 111 532 571 610 650 689 727 766 805 844 883 ** U 09 112 922 961 999 *038 *077 *115 *154 *192 *231 *269 1 4:1 4.0 3.9 113 05308 346 385 423 461 500 638 576 614 652 2 8, 8.0 7.8 114 690 729 767 805 843 881 918 956 994 *032 3 12.3 12.0 11.7 115 06070 108 145 183 221 258 296 333 371 408 4 16.4 16.0 15.6 116 446 483 521 558 ^595 633 670 707 744 781 5 6 20..5 24.6 20.0 24.0 19.5 23.4 117 819 856 893 930 *967 *004 *041 *078 *115 *151 7 28.7 28.0 27.3 118 07188 225 262 298 335 372 408 445 482 518 8 32.8 32.0 31.2 119 555 591 628 664 700 737 773 809 846 882 9 36.9 36.0 35.1 120 918 954 990 *027 *063 *099 *135 *171 *207 *243 121 08279 314 350 386 422 458 493 529 565 600 SB 3Y at) 122 636 672 707 743 778 814 849 884 920 955 1 3.8 3.7 g~g 123 991 *026 *061 *096 *132 *167 *202 *237 *272 *307 2 7.6 7.4 7*.2 124 09342 377 412 447 482 517 652 687 621 656 3 11.4 11.1 10.8 125 691 726 760 795 830 864 899 934 968 *003 4 15.2 14.8 14.4 126 10037 072 106 140 175 209 243 278 312 346 5 6 19.0 22.8 18.5 22.2 18.0 21.6 127 380 415 449 483 517 551 585 619 653 687 7 26.6 25.9 25.2 128 129 721 11059 755 093 789 126 823 160 857 193 890 ~22T h924 261 958 294 992 327 *025 361 8 9 30.4 34.2 29.6 33.3 28.8 32.4 130 394 428 461 494 528 561 594 628 661 694 131 727 760 793 826 860 893 926 959 992 *024 35 34 33 132 12057 090 123 156 189 222 254 287 320 352 1 3.5 3.4 3.3 133 385 418 450 483 516 548 681 613 646 678 2 7.0 6.8 6.6 134 710 743 775 808 840 872 905 937 969 *001 3 10.5 10.2 9.9 135 13033 066 098 130 162 194 226 258 290 322 4 14.0 13.6 13.2 136 354 386 418 450 481 513 645 677 609 640 5 17.5 17.0 16.5 6 21.0 20.4 19.8 137 672 704 735 767 799 830 862 893 925 956 7 24.5 23.8 23.1 138 988 *019 *051 *082 *114 *145 *176 *208 *239 *270 8 28.0 27.2 26.4 139 14301 333 364 395 426 457 489 520 551 582 9 31.5 30.6 29.7 140 613 644 675 706 737 768 799 829 860 891 1 V /3.2 31 3.1 30 3.0 141 142 922 15229 953 259 983 290 *014 320 *045 351 *076 381 412 *137 442 *168 473 *198 503 143 634 564 594 625 655 685 7HT 746 776 806 2 6.4 6.2 6.0 144 836 866 897 927 957 987 *017 ^047 *077 *107 3 9.6 9.3 9.0 145 16137 167 197 227 256 286 316 346 376 406 4 12.8 12.4 12.0 146 435 465 495 524 554 584 613 643 673 702 5 16.0 15.5 15.0 6 19.2 18.6 18.0 147 732 761 791 820 850 879 909 938 967 997 7- 22.4 21.7 21.0 148 17026 056 085 114 143 173 202 231 260 289 8 25.6 24.8 24.0 149 319 348 377 406 435 464 493 522 551 580 9 28.8 27.9 27.0 150 609 638 667 696 725 754 782 811 840 869 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 150 Logarithms of Numbers 200 3.01 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 150 17609 638 667 696 725 754 782 811 840 869 1 2 3 4 5 6 7 S 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 S 9 1 2 3 4 5 6 7 8 9 29 2.9 5.8 8.7 11.6 14.5 17.4 20.3 23.2 26.1 27 2.7 5.4 8.1 10.8 13.5 16.2 18.9 21.6 24.3 25 2.5 5.0 7.5 10.0 12.5 15.0 "17.5 20.0 22.5 23 2.3 4.6 6.9 9.2 11.5 13.8 16.1 18.4 20.7 21 2.1 4.2 6.3 8.4 10.5 12.6 14.7 16.8 18.9 28 2.8 5.6 8.4 11.2 14.0 16.8 19.6 22.4 25.2 26 2.6 : 5.2 10.4. 13.0 ' 15.6 18.2 20.8 23.4 24 2.4 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 22 2.2 , 4.4 6.6 8.8 11.0 13.2 15.4 17.6 19.8 151 152 153 154 155 156 157 158 159 898 18184 469 752 19033 312 590 866 20140 926 213 498 780 061 340 618 893 167 955 241 526 808 089 368 645 921 194 984 270 554 837 117 396 673 948' 222 *013 298 583 865 145 424 700 976 249 *041 327 611 893 173 451 728 *003 276 *070 355 639 921 201 479 756 *030 303 *099 384 667 949 229 507 783 *058 330 *127 412 696 977 257 535 811 *085 358 *156 441 724 *005 285 562 838 *112 385 160 412 439 466 493 520 548 575 602 629 656 161 162 163 164 165 166 167 168 169 683 952 21219 484 748 22011 272 531 789 710 978 245 511 775 037 298 557 814 737 *005 272 537 J&OJ. 063 324 583 840 763 *032 299 564 827 089 350 608 866 790 *059 325 590 854 115 376 634 891 817 *085 352 617 880 141 401 660 917 844 *112 378 643 906 167 427 686 943 871 *139 405 669 932 194 453 712 968 898 *165 431 696 958 220 479 737 994 925 *192 458 722 985 246 505 763 *019 170 23045 070 096 121 147 172 198 223 249 274 171 172 173 174 175 176 177 178 179 300 553 805 24055 304 551 797 25042 285 325 578 830 080 329 576 822 066 310 350 603 855 105 353 601 846 091 334 376 629 880 130 378 625 871 115 358 401 654 905 155 403 650 895 139 382 426 679 930 180 428 674 920 164 406 452 704 955 204 452 699 944 188 431 477 729 980 229 477 724 969 212 455 502 754 *005 254 502 748 993 237 479 528 779 *030 279 627 773 *018 261 503 180 527 551 575 600 624 648 672 696 720 744 181 182 183 184 185 186 187 188 189 768 26007 245 482 717 951 27184 416 646 792 031 269 505 741 975 207 439 669 816 055 293 529 764 998 231 462 692 840 079 316 553 788 *021 254 485 715 864 102 340 576 811 *045 277 508 738 888 126 364 600 834 *068 300 531 761 912 150 387 623 858 *091 323 554 784 935 174 411 647 881 *114 346 577 807 959 198 435 670 905 *138 370 600 830 983 221 458 694 928 *161 393 623 852 190 875 898 921 944 967 989 *012 *035 *058 *081 191 192 193 194 195 196 197 198 199 28103 330 556 780 29003 226 447 667 885 126 353 578 803 026 248 469 688 907 149 375 601 825 048 270 491 710 929 171 398 623 847 070 292 513* 732 951 194 421 646 870 092" 314 535 754 973 217 443 668 892 115 336 557 776 994 240 466 691 914 137 358 579 70S *016 262 488 713^ 93V 159 380 601 820 *038 285 511 735 959 181 403 623 842 *060 307 533 758 981 203 425 645 863 *081 200 30 103 125 146 168 190 211 233 255 276 298 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 200 Logarithms of Numbers 250 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 200 30 103 125 146 168 190 211 233 255 276 298 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 7 i 2 3 .4. 5 6 7 8 9 os 2 50102 22; 2.2 4.4 6.6 8.8 11.0 13.2 15.4 17.6 19.8 20 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 18 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 99957 21 2.1 4.2 6.3 8.4 10.5 12.6 14.7 16.8 18.9 yp 1.9 3.8 5.7 7.6 9.5 11.4 13.3 15.2 17.1 17 1.7 3.4 5,1 6.8 8.5 10.2 11.9 13.6 15.3 201 202 203 204 205 206 207 208 209 320 535 750 963 31 175 387 597 806 32015 341 557 771 984 197 408 618 827 035 363 578 792 *006 218 429 639 848 056 384 600 814 *027 239 450 660 869 077 406 621 835 *048 260 471 681 890 098 428 643 856 *069 281 492 702 911 118 449 664 878 *091 302 513 723 931 139 471 685 899 *112 323 534 744 952 160 492 707 920 *133 345 555 ^765 Sf 514 728 942 *154 366 576 *785. 994 201 210 222 243 263 284 305 325 346 366 387 408 211 212 213 214 215 216 217 218 219 428 634 838 33041 244 445 646 846 34044 449 654 858 062 264 465 666 866 064 469 675 879 082 284 486 686 885 084 490 695 899 102s 304 506 706 905 104 510 715 919 122 325 526 726 925 124 531 736 940 143 345 546 746 945 143 552 756 960 163 365 566 766 965 163 572 777 980 183 385 586 786 985 183 593 797 *001 203 405 606 806 *005 203 613 818 *021 224 425 626 826 *025 223 220 242 262 282 301 321 341 361 380 400 420 221 222 223 224 225 226 227 228 229 439 635 830 35025 218 411 603 793 984 459 655 850 044 238 430 622 813 *003 479 674 869 064 257 449 641 832 *021 498 694 889 083 276 468 660 851 *040 518 713 908 102 295 488 679 870 *059 537 733 928 122 315 507 698 889 *078 557 753 947 141 334 526 717 908 *097 577 772 967 160 353 545- 736 927 *116 596 792 986 180 372 564 755 946 *135 616 811 *005 199 392 583 774 965 *154 230 36173 192 211 229 248 267 286 305 324 342 231 232 233 234 235 236 237 238 239 361 549 736 922 37107 291 475 658 840 380 568 754 940 125 310 493 676 858 399 586 773 959 144 328 511 694 876 418 605 791 977 162 346 530 712 894 436 624 810 996 181 365 548 731 912 455 642 829 *014 199 383 566 749 931 474 661 847 *033 218 401 585 767 949 493 680 866 *051 236 420 603 785 967 511 698 884 *070 254 438 621 803 985 530 717 903 *088 273 457 639 822 *003 240 38021 039 057 075 093 112 130 148 166 184 241 242 243 244 245 246 247 248 249 202 382 561 739 917 39094 270 445 620 220 399 578 757 934 111 287 463 637 238 417 596 775 952 129 305 480 655 256 435 614 792 970 146 322 498 672 274 453 632 810 987 164 340 515 690 292 471 650 828 *005 182 358 533 707 31Q_ 489 668 846 *023 199 375 550 724 328 507 686 863 *041 217 393 568 742 346 525 703 881 *058 235 410 585 759 364 543 721 899 *076 252 428 602 777 250 794 811 829 846 863 881 898 915 933 950 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. n 50 Logarithms of Numbers 300^- (90 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 250 39794 811 829 846 863 881 898 915 933 950 1 2 3 4 5 6 7 8 9 J =1 =1 1 2 3 4 5 5 7 8 9 1 2 3 4 5 6 7 8 9 18 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 \t 3g w e 3glO 2. 13429 16. i.6 3.2 4.8 6.4 8.0 9.6 11.2 12.8 14.4 14 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11.2 12.6 f* 3.4 5.1 6.8 8.5 10.2 11.9 13.6 15.3 ris- 44819 15 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 251 252 253 254 255 256 257 258 259 967 40140 312 483 654 824 993 41 162 330 985 157 329 500 671 841 *010 179 347 *002 175 346 518 688 858 *027 196 363 *019 192 364 535 705 875 *037 209 381 552 722 892 *054 226 398 569 739 909 *078 246 414 *071 243 415 586 756 926 *095 263 430 *088 261 432 603 773 943 *111 280j 4*7- *106 278 449 620 790 960 *128 296 ,464 *123 295 466 637 807 976 *145 313 481 ~647~ *044 212 380 .*061 22& 397 260 497 514 531 547 564 581 597 614 '631 261 262 263 264 265 266 267 268 269 664 830 996 42160 325 488 651 813 975 681 847 *012 177 341 504 667 830 991 697 863 *029 193 357 521 684 846 *008 714 880 *045 210 374 537 700 862 *024 731 896 *062 226 390 553 716 878 *040 747 913 *078 243 406 570 732 894 *056 764 929 *095 259 423 586 749 911 *072 780 946 *111 275 439 602 765 927 *088 797 963 *127 292 455 619 781 943 *104 814 979 *144 308 472 635 797 959 *120 270 43136 152 169 185 201 217 233 249 265 281 271 272 273 274 275 276 277 278 279 297 457 616 775 933 44091 248 404 560 313 473 632 791 949 107 264 420 576 329 489 648 807 965 122 279 436 592 345 605 664 823 981 138 295 451 607 361 521 680 838 996 154 311 467 623 377 537 696 854 *012 170 326 483 638 393 553 712 870 *028 185 342 498 654 409 569 727 886 *04)t 201 358 514 669 425 584 743 902 *059 217 373 529 685 441 600 759 917 *075 232 389 545 700 280 716 731 747 762 778 793 809 824 840 855 281 282 283 284 285 286 287 288 289 871 45025 179 332 484 637 788 939 46090 886 040 194 347 500 652 803 954 105 902 056 209 362 515 667 818 969 120 917 071 225 378 530 682 834 984 135 932 086 240 393 545 697 849 *000 150 948 102 255 408 561 712 864 *015 165 963 117 271 423 576 728 879 *030 180 979 133 286 439 591 743 894 *045 195 994 148 301 454 606 758 909 *060 210 *010 163 317 469 621 773 924 *075 225 290 240 255 270 285 300 315 330 345 359 374 291 292 293 294 295 296 297 298 299 389 538 687 835 982 47129 276 422 567 404 553 702 850 997 144 290 436 582 419 568 716 864 *012 159 305 451 596 434 583 731 879 *026 173 319 465 611 449 598 746 894 *041 188 334 480 625 464 613 761 909' *056 202 349 494 640 479 627 '776 ~923 *070 217 363 509 654 494 642 790 938 *085 232 378 524 669 509 657 805 953 *100 246 392 538 683 523 672 820 967 *114 261 407 553 698 300 712 727 741 756 770 784 799 813 828 842 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 300 Logarithms of Numbers 350 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 300 47712 727 741 756 770 784 799 813 828 842 1 =.4 I =.4 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 og3 t7712 Og IT 19714 15 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 13 1.3 2.6 3.9 6.2 6.5 7.8 9.1 10.4 11.7 12547 38727 14 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11.2 12.6 12- 1.2 2.4 3.6 4.8 6.0 7.2 8.4 9.6 10.8 301 302 303 304 305 306 307 308 309 857 48001 144 287 430 572 714 855 996 871 015 159 302 444 686 728 869 *010 885 029 173 316 458 601 742 883 *024 900 044 187 330 473 615 756 897 *038 914 058 202 344 487 629 770 911 *052 929 073 216 359 501 643 785 926 *066 943 087 230 373 515 657 799 940 *080 958 101 244 387 530 671 813 954 *094 972 116 259 401 544 686 827 968 *108 986 130 273 416 558 700 841 982 *122 310 49 136 150 164 178 192 206 220 234 248 262 311 312 313 314 315 316 317 318 319 276 415 554 693 831 969 50106 243 379 290 429 568 707,. 304 443 582 721 859 996 133 270 406 318 457 696 734 872 *010 147 284 420 332 471 610 748 886 *024 161 297 433 346 485 624 762 900 *037 174 311 447 360 499 638 776 914 *051 188 325 461 374 513 651 790 927 *065 202 338 474 388 527 665 803 941 *079 215 352 488 402 541 679 817 955 *092 229 365 501 845 982 120 256 393 320 515 629 542 556 669 583 696 610 623 637 321 322 323 324 325 326 327 328 329 651 786 920 51055 188 322 _ 455 587 720 664 799 934 068 202 335 468 601 733 678 813 947 081 215 348 481 614 746 691 826 961 095 228 362 495 627 759 705 840 974 108 242 375 608 640 772 718 853 987 121 255 388 521 654 786 732 866 *001 135 268 402 534 667 799 745 880 *014 148 283 415 648 680 812 759 893 *028 162 295 428 561 693 825 772 907 *041 175 308 441 574 706 838 330 851 865 878 891 904 917 930 943 957 970 331 332 333 334 335 336 337 338 339 983 52114 244 375 504 634 763 892 53020 996 127 257 388 517 647 776 905 033 *009 140 270 401 530 660 789 917 046 *022 153 284 414 543 673 802 930 058 *035 166 297 427 556 686 815 943 071 *048 179 310 440 569 699 827 956 084 *061 192 323 453 682 711 840 969 097 *075 205 336 466 595 724 853 982 110 *088 218 349 479 608 737 866 994 122 *101 231 362 492 621 750 879 *007 135 340 148 161 173 186 199 212 224 237 250 263 341 342 343 344 345 346 347 348 349 275 403 629 656 782 908 54033 158 283 288 415 542 668 794 920 045 170 295 301 428 555 681" 807 933 058 183 307 314 441 667 694 820 945 070 195 320 326 453 580 706 832 958 083 208 332 339 466 593 719 845 970 095 220 345 352 479 605 732 857 983 108 233 357 364 491 618 744 870 996 120 245 370 377 504 631 757 882 *008 133 258 382 390 517 643 769 895 *020 145 270 394 350 407 419 432 444 456 469 481 494 506 518 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 350 Logarithms of Numbers 400 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 350 54407 419 432 444 456 469 481 494 506 518 s ^^ 13, 1 1.3 2 2.6 3 3.9 4 5-.2 3 6.5 6 7.8 7 9.1 8 10.4 9 11.7 1 12 1.2 2.4 3.6 4.8 6.0 7.2 8.4, 9.6 10.8 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 351 352 353 354 355 356 357 358 359 531 654 777 900 55023 145 267 388 509 543 667 790 913 035 157 279 400 522 555 679 802 925 047 169 291 413 534 568 691 814 937 060 182 303 425 546 580 704 827 949 072 194 315 437 558 593 716 839 962 084 206 328 449 570 605 728 851 974 096 218 340 461 582 617 741 864 986 108 230 352 473 594 630 753 876 998 121 242 364 485 606 642 765 888 *011 133 255 376 497 618 360 630 642 654 666 678 691 703 715 727 739 361 362 363 364 365 366 367 368 369 751 871 991 56110 229 348 467 585 703 763 883 *003 122 241 360 478 597 714 775 895 *015 134 253 372 490 608 726 787 907 *027 146 265 384 502 620 738 799 919 *038 158 277 396 514 632 750 811 931 *050 170 289 407 526 644 761 823 943 *062 182 301 419 538 656 773 835 955 *074 194 312 431 549 667 785 847 967 *086 205 324 443 561 679 797 859 979 *098 217 336 455 573 691 808 370 820 832 844 855 867 879 891 902 914 926 //^ 11- 1 1.1 2 2.2 3 3.3 4 4.4 5 5.5 6 6A 7 7.7 8 8.8 9 9.9 371 372 373 374 375 376 377 378 379 937 57054 171 287 403 519 634 749 864 949 066 183 299 415 530 646 761 875 961 078 194 310 426 542 657 772 887 972 089 206 322 438 553 669 784 898 984 101 217 334 449 565 680 795 910 996 113 229 345 461 576 692 807 921 *008 124 241 357 588 703 818 933 *019 136 252 368 1484 600 715 830 944 *031 148 264 380 496 611 726 841 955 *043 159 276 392 507 623 738 852 967 380 978 990 *001 *013 *024 *035 *047 *058 *070 *081 381 382 383 384 385 386 387 388 389 58092 206 320 433 546 659 771 883 995 104 218 331 444 557 670 782 894 *006 115 229 343 456 569 681 794 906 *017 127 240 354 467 580 692 805 917 *028 138 252 365 478 591 704 816 928 *040 149 263 377 490 602 715 827 939 *051 161 274 388 501 614 726 838 950 *062 172 286 399 512 625 184 297 410 624 636 195 309 422 535 647 760 872 984 *095 -737" 850 961 *073 749 861 973 *084 390 59106 118 129 140 151 162 173 184 195 207 391 392 393 394 395 396 397 398 399 218 329 439 550 660 770 879 988 60097 229 340 450 561 671 780 890 999 108 240 351 461 572 682 791 901 *010 119 251 362 472 583 693 802 912 *021 130 262 373 483 594 704 813 923 *032 141 273 384 494 605 715 824 934 *043 152 284 395 506 616 726 835 945 *054 163 295 406 517 627 737 846 956 *065 173 306 417 528 638 748 857 966 *076 184 318 428 539 649 759 868 977 *086 195 400 206 217 228 239 249 260 271 282 293 304 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 400 Logarithms of Numbers 450 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 400 60206 217 228 239 249 260 271 282 293 304 1 2 3 4 5 6 T 8 9 Ic =lc =9 1 2 3 4 5 6 7 8 9 11 1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 g M S [lo 6377 10 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 10 * 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 ge] 8431 401 402 403 404 405 406 407 408 409 314 423 531 638 746 853 959 61066 172 325 433 541 649 756 863 970 077 183 336 444 552 660 767 874 981 087 194 347 455 563 670 778 885 991 098 204 358 466 574 681 788 895 *002 109 215 369 477 584 692 -Z9& 379 487 595 703 810 917 *023 130 236 390 498 606 713 821 927 *034 140 247 401 509 617 724 831 938 *045 151 257 412 520 627 735 842 949 *055 162 268 906 *013 119 225 410 278 289 300 310 321 331 342 352 363 374 411 412 413 414 415 416 417 418 419 384 490 595 700 805 909 62014 118 221 395 500 606 711 815 920 024 128 232 405 511 616 721 826 930 034 138 242 416 521 627 731 836 941 045 149 252 426 532 637 742 847 951 055 159 263 437 542 648 752 857 962 066 170 273 448 553 658 763 868 972 076 180 284 458 563 669 773 878 982 086 190 294 469 574 679 784 888 993 097 201 304 479 584 690 794 899 *003 107 211 315 420 325 335 346 356 366 377 387 397 408 418 421 422 423 424 425 426 427 428 429 428 531 634 737 839 941 63043 144 246 439 542 644 747 849 951 053 155 256 449 552 655 757 859 961 063 165 266 459 562 665 767 870 972 073 175 276 469 572 675 778 880 982 083 185 286 480 583 685 788 890 992 094 195 296 490 593 696 798 900 *002 104 205 306 500 603 706 808 910 *012 114 215 317 511 613 716 818 921 *022 124 225 327 521 624 726 829 931 *033 134 236 337 430 347 357 367 377 387 397 407 417 428 438 431 432 433 434 435 436 437 438 439 448 548 649 749 849 949 64048 147 246 458 558 659 759 859 959 058 157 256 468 568 669 769 869 969 068 167 266 478 579 679 779 879 979 078 177 276 488 689 689 789 889 988 088 187 286 498 599 699 799 899 998 098 197 296 508 609 709 809 909 *008 108 207 306 518 619 719 819 919 *018 118 217 316 528 629 729 829 929 *028 128 227 326 538 639 739 839 939 *038 137 237 335 440 345 355 365 375 385 395 404 414 424 434 441 442 443 444 445 446 447 448 449 444 542 640 738 836 933 65031 128 225 454 552 650 748 846 943 040 137 234 464 562 660 758 856 953 050 147 244 473 572 670 768 865 963 060 157 254 483 582 680 777 875 972 070 167 263 493 591 689 787 885 982 079 176 273 503 601 699 797 895 992 089 186 283 513 611 709 807 904 *002 099 196 292 523 621 719 816 914 *011 108 205 302 532 631 729 826 924 *021 118 215 312 450 321 331 341 350 360 369 379 389 398 408 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. I] 450 Logarithms of Numbers 500 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 450 65321 331 341 350 360 369 379 389 398 408 451 418 427 437 447 456 466 475 485 495 504 452 514 523 533 543 552 562 571 581 591 600 453 610 619 629 639 648 658 667 677 686 696 454 706 715 725 734 744 753 763 772 782 792 455 801 811 820 830 839 849 858 868 877 887 456 896 906 916 925 935 944 954 963 973 982 457 992 *001 *011 *020 *030 *039 *049 *058 *068 *077 458 66087 096 106 115 124 134 143 153 162 172 459 181 191 200 210 219 229 238 247 257 266 460 276 285 295 304 314 323 332 342 351 361 mA ' 1 461 462 370 464 380 474 389 483 398 492 408 502 417 511 427 521 436 630 445 539 455 549 10 1 1.0 &. 463 658 567 577 586 596 605 614 624 633 642 2 2.0 464 652 661 671 680 689 699 708 717 727 736 T' 3.0 2?F 465 745 755 764 773 783 792 801 811 820 829 4 4.0 3.6 466 839 848 857 867 876 885 894 904 913 922 5 5.0 4.5 6 6.0 5.4 467 932 941 950 960 969 978 987 997 *006 *015 7 7.0 6.3 468 67025 034 043 052 062 071 080 089 099 108 8 8.0 7.2 469 117 127 136 145 154 164 173 182 191 201 9 9.0 8.1 470 210 219 228 237 247 256 265 274 284 293 471 302 311 321 330 339 348 357 367 376 385 472 394 4P3 413 422 431 440 449 459 468 477 473 486 495 504 514 523 532 541 550 560 569 474 578 587 596 605 614 624 633 642 651 660 475 669 679 688 697 706 715 724 733 742 752 476 761 770 779 788 797 806 815 825 834 843 477 852 861 870 879 888 897 906 916 925 934 478 943 952 961 970 979 988 997 *006 *015 *024 479 68034 043 052 061 070 079 088 097 106 115 480 124 133 142 151 160 169 178 187 196 205 481 215 224 233 242 251 260 269 278 287 296 8 482 305 314 323 332 341 350 359 368 377 386 1 0.8 483 395 404 413 422 431 440 449 458 467 476 2 1. 6 484 485 494 502 511 520 629 538 547 556 565 3 2.4 485 574 583 592 601 610 619 628 637 646 655 4 3. 2 486 664 673 681 690 699 708 717 726 735 744 540 6 4. S 487 753 762 771 780 789 797 806 815 824 833 7 5.6 488 842 851 860 869 878 886 895 904 913 922 8 6.4 489 931 940 949 958 966 975 984 993 *002 *011 9 72 490 69020 028 037 046 055 064 073 082 090 099 491 108 117 126 135 144 152 161 170 179 188 492 197 205 214 223 232 241 249 258 267 276 493 285 294 302 311 320 329 338 346 355 364 494 373 381 390 399 408 417 425 434 443 452 495 461 469 478 487 496 504 513 522 531 539 496 548 557 566 574 583 592 601 609 618 627 497 636 644 653 662 671 679 688 697 705 714 498 723 732 740 749 758 767 775 784 793 801 499 810 819 827 836 845 854 862 871 880 888 500 897 906 914 923 932 940 949 958 966 975 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 10 500 Logarithms of Numbers 550 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 500 69897 906 914 923 932 940 949 958 966 975 log 5 =.69897 00043 9 8 1 0.9 0.8 2 1.8 1.6 3 2.7 2.4 . 4 3.6 3.2' 5 4.5 4.0 6 5.4 4.8 7 6.3 5.6 8 7.2 6.4 9 8.1 7.2 7 1 0.7 2 1.4 3 2.1 4 2.8 6 3.5 6 4.2 7 4.9 8 5.6 9 6.3 501 502 503 504 505 506 507 508 509 984 70070 157 243 329 415 501 586 672 992 079 165 252 338 424 509 595 680 *001 088 174 260 346 432 618 603 689 *010 096 183 269 355 441 526 612 697 *018 105 191 278 364 449 535 621 706 *027 114 200 286 372 458 544 629 714 *036 122 209 295 381 467 552 638 723 *044 131 217 303 389 475 561 646 731 *053 140 226 312 398 484 569 655 740 *062 148 234 321 406 492 678 663 749 510 757 766 774 783 791 800 808 817 825 834 511 512 513 514 515 516 517 518 519 842 927 71012 096 181 265 349 433 517 851 935 020 105 189 273 357 441 525 859 944 029 113 198 282 366 450 633 868 952 037 122 206 290 374 458 542 876 961 046 130 214 299 383 466 550 885 969 054 139 223 307 391 475 559 893 978 063 147 231 315 399 483 567 902 986 071 155 240 324 408 492 575 910 995 079 164 248 332 416 500 584 919 *003 088 172 257 341 425 508 592 520 600 609 617 625 634 642 650 659 667 675 521 522 523 524 525 526 527 528 529 684 767 850 933 72016 099 181 263 346 692 775 858 941 024 107 189 272 354 700 784 867 950 032 115 198 280 362 709 792 875 958 041 123 206 288 717 800 883 966 049 132 214 296 378 725 809 892 975 057 140 222 304 387 734 817 900 983 066 148 230 313 395 742 825 908 991 074 156 239 321 403 750 834 917 999 082 165 247 329 411 759 842 925 *008 090 173 255 337 419 370' 530 428 436 444 452 460 469 477 485 493 501 531 532 533 534 535 636 537 538 539 509 591 673 754 835 916 997 73078 159 518 599 681 762 843 925 *006 086 167 526 607 689 770 852 933 *014 094 175 534 616 697 779 860 941 *022 102 183 542 624 705 787 868 949 *030 111 191 550 632 713 795 876 957 *038 4A?- 558 640 722 803 884 965 *046 127 207 567 648 730 811 892 973 *054 135 215 575 656 738 819 900 981 *062 143 223 583 665 746 827 908 989 *070 151 231 ISST 540 239 247 255 263 272 280 288 296 304 312 541 542 543 544 545 546 547 548 549 320 400 480 560 640 719 799 878 957 328 408 488 668 648 727 807 886 965 336 416 496 576 656 735 815 894 973 344 424 504 584 664 743 823 902 981 352 432 512 592 672 751 830 910 989 360 440 520 600 679 759 838 918 997 368 448 528 608 687 767 846 926 *005 376 456 536 616 695 775 854 933 *013 384 464 544 624 703 783 862 941 *020 392 472 552 632 711 791 870 949 *028 550 74036 044 052 060 068 076 084 092 099 107 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 550 Logarithms of Numbers 600 11 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 550 74036 044 052 060 068 076 084 092 099 107 551 115 123 131 139 147 155 162 170 178 186 552 194 202 210 218 225 233 241 249 257 265 553 273 280 288 296 304 312 320 327 335 343 554 351 359 367 374 382 390 398 406 414 421 555 429 437 445 453 461 468 476 484 492 500 556 507 515 523 531 539 547 554 562 570 578 557 586 593 601 609 617 624 632 640 648 656 558 559 663 741 671 749 679 757 687 7G4 m .702 780 710 788 718 796 726 803 733 811 560 819 827 834 842 850 858 865 873 881 889 561 896 904 912 920 927 935 943 950 958 966 562 974 981 989 997 *005 *012 *020 *028 *035 *043 563 75051 059 066 074 082 089 097 105 113 120 564 128 136 143 151 159 166 174 182 189 197 565 205 213 220 228 236 243 251 259 266 274 566 282 289 297 305 312 320 328 335 343 351 567 358 366 374 381 389 397 404 412 420 427 568 435 442 450. 458 465 473 481 488 496 504 569 511 519 5%L 534 542 549 557 565 572 580 570 587 595 603 610 ,618 626 633 641 648 656 8mm 571 664 671 679 686 694 702 709 717 724 732 7 572 740 747 755 762 770 778 785 793 800 808 1 0.8 0.7 573 815 823 831 838 846 853 861 868 876 884 2 1.6 1.4 574 891 899 906 914 921 929 937 944 952 959 3 2.4 2.1 575 967 974 982 989 997 *005 *012 *020 *027 *035 4 3.2 2.8 5 A f\ OK 576 76042 050 057 065 072 080 087 095 103 110 4.U o.o 6 4.8 4.2 577 118 125 133 140 148 155 163 170 178 185 7 5.6 4.9 578 193 200 208 215 223 230 238 245 253 260 8 6.4 5.6 579 268 275 283 290 298 305 313 320 328 335 9 7.2 6.3 580 343 350 358 365 373 380 388 395 403 410 581 418 425 433 440 448 455 462 470 477 485 582 492 500 507 515 522 530 537 545 552 559 583 567 574 582 589 597 604 612 619 626 634 584 641 649 656 664 671 678 686 693 701 708 585 716 723 730 738 745 753 760 768 775 782 586 790 797 805 812 819 827 834 842 849 856 587 864 871 879 886 893 901 908 916 923 930 588 938 945 953 960 967 975 982 989 997 *004 589 77012 019 026 034 041 048 056 063 070 078 590 085 093 100 107 115 122 129 137 144 151 591 159 166 173 181 188 195 203 210 217 225 592 232 240 247 254 262 269 276 283 291 298 593 305 313 320 327 335 342 349 357 364 371 594 379 386 393 401 408 415 422 430 437 444 595 452 459 466 474 481 488 495 503 510 517 596 525 532 539 546 554 561 568 576 583 590 597 597 605 612 619 627 634 641 648 656 663 598 670 677 685 692 699 706 714 721 728 735 599 743 750 757 764 772 779 786 793 801 808 600 815 822 830 837 844 851 859 866 873 880 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 12 600 Logarithms of Numbers 650 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 600 77815 822 830 837 844 851 859 866 873 880 601 887 895 902 909 916 924 931 938 945 952 602 960 967 974 981 988 996 *003 *010 *017 *025 603 78032 039 046 053 061 068 075 082 089 097 604 104 111 118 125 132 140 147 154 161 168 605 176 183 190 197 204 211 219 226 233 240 606 247 254 262 269 276 283 290 297 305 312 607 319 326 333 340 347 355 362 369 376 383 608 390 398 405 412 419 426 433 440 447 455 609 462 469 476 483 490 497 504 512 519 526 610 533 540 547 554 561 569 576 583 590 597 8fm 611 604 611 618 625 633 640 647 654 661 668 7 612 675 682 689 696 704 711 718 725 732 739 I 0.8 0.7 613 746- 753 760 767 774 781 789 796 803 810 2 1.6 1.4 614 817 824 831 838 845 852 859 866 873 880 3 2.4 2.1 615 888 895 902 909 916 923 930 937 944 951 4 3.2 2.8 616 958 965 972 979 986 993 *000 *007 *014 *021 5 4.0 3.5 6 4.8 4.2 617 79029 036 043 050 057 064 071 078 085 092 7 5.6 4.9 618 099 106 113 120 127 134 141 148 155 162 8 6.4 5.6 619 169 176 183 190 197 204 211 218 225 232 9 7.2 6.3 620 239 246 253 260 267 274 281 288 295 302 621 309 316 323 330 337 344 351 358 365 372 622 379 386 393 400 407 414 421 428 435 442 623 449 456 463 470 477 484 491 498 505 511 624 518 525 532 539 546 553 560 567 574 581 625 588 595 602 609 616 623 630 637 644 650 626 657 664 671 678 685 692 699 706 713 720 627 727 734 741 748 754 761 768 775 782 789 628 796 803 810 817 824 831 837 844 851 858 629 865 872 879 886 893 900 906 913 920 927 630 934 941 948 955 962 969 975 982 989 996 631 80003 010 017 024 030 037 044 051 058 065 6 632 072 079 085 092 099 106 113 120 127 134 1 0.6 633 140 147 154 161 168 175 182 188 195 202 2 1.2 634 209 216 223 229 236 243 250 257 264 271 3 1.8 635 277 284 291 298 305 312 318 325 332 339 4 2.4 636 346 353 359 366 373 380 387 393 400 407 5 3.0 6 3.6 637 414 421 428 434 441 448 455 462 468 475 7 4.2 638 482 489 496 502 509 516 523 530 536 543 8 4.8 639 550 557 564 570 577 584 591 598 604 611 9 5.4 640 618 625 632 638 645 652 659 665 672 679 641 686 693 699 706 713 720 726 733 740 747 642 754 760 767 774 781 787 794 801 808 814 643 821 828 835 841 848 855 862 868 875 882 644 889 895 902 909 916 922 929 936 943 949 645 956 963 969 976 983 990 996 *003 *010 *017 646 81023 030 037 043 050 057 064 070 077 084 647 090 097 104 111 117 124 131 137 144 151 648 158 164 171 178 184 191 198 204 211 218 649 224 231 238 245 251 258 265 271 278 285 650 291 298 305 311 318 325 331 338 345 351 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. I] 650 Logarithms of Numbers 700 13 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 650 81291 298 305 311 318 325 331 338 345 351 651 358 365 371 378 385 391 398 405 411 418 652 425 431 438 445 451 458 465 471 478 485 653 491 498 505 511 518 525 531 538 544 551 654 558 564 571 578 584 591 598 604 611 617 655 624 631 637 644 651 657 664 671 677 684 656 690 697 704 710 717 723 730 737 743 750 657 757 763 770 776 783 790 796 803 809 816 658 823 829 836 842 849 856 862 869 875 882 659 889 895 902 908 915 921 928 935 941 948 660 954 961 968 974 981 987 994 *000 *007 *014 661 82020 027 033 040 046 053 060 066 073 079 662 086 092 099 -105 112 119 125 132 138 145 663 151 158 164 171 178 184 191 197 204 210 664 217 223 230 236 243 249 256 263 269 276 665 282 289 295 302 308 315 321 328 334 341 666 347 354 360 367 373 380 387 393 400 406 667 413 419 426 432 439 445 452 458 465 471 668 478 484 491 497 504 510 517 523 530 536 669 543 549 556 562 569 575 582 588 595 601 670 607 614 620 627 633 640 646 653 659 666, 671 672 679 685 692 698 705 711 718 724 730 T 6 672 737 743 750 756 763 769 776 782 789 795 1 0.7 0.6 673 802 808 814 821 827 834 840 847 853 860 2 1.4 1.2 674 866 872 879 885 892 898 905 911 918 924 3 2.1 1.8 675 930 937 943 950 956 963 969 975 982 988 4 2.8 2.4 676 995 *001 *008 *014 *020 *027 *033 *040 *046 *052 5 3.5 3.0 6 4.2 3.6 677 83059 065 072 078 085 091 097 104 110 117 7 4.9 4.2 678 123 129 136 142 149 155 161 168 174 181 8 5.6 4.8 679 187 193 200 206 213 219 225 232 238 245 9 6.3 5.4 680 251 257 264 270 276 283 289 296 302 308 681 315 321 327 334 340 347 353 359 366 372 682 378 385 391 398 404 410 417 423 429 436 683 442 448 455 461 467 474 480 487 493 499 684 506 512 518 525 531 537 544 550 556 f 563 685 569 575 582 588 594 601 607 613 620' 626 686 632 639 645 651 658 664 670 677 683 689 687 696 702 708 715 721 727 734 740 746 753 688 759 765 771 778 784 790 797 803 809 816 689 822 828 835 841 847 853 860 866 872 879 690 885 891 897 904 910 916 923 929 935 ~942~ 691 948 954 960 967 973 979 985 992 998 *004 692 84011 017 023 029 036 042 048 055 061 067 693 073 080 086 092 098 105 111 117 123 130 694 136 142 148 155 161 167 173 180 186 192 695 198 205 211 217 223 230 236 242 248 255 696 261 267 273 280 286 292 298 305 311 317 697 323 330 336 -342 348 354 361 367 373 379 698 386 392 398 404 410 417 423 429 435 442 699 448 454 460 466 473 479 485 491 497 504 700 510 516 522 528 535 541 547 553 559 566 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 14 700 Logarithms of Numbers 750 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 700 84510 516 522 528 535 541 547 553 559 566 log 7 =.8450 7 1 0.7 2 1.4 3 2.1 4 2.8 5 3.5 6 4.2 7 4.S 8 5.6 9 6.3 1 2 3 4 5 6 7 8 9 80400 j 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6 3.6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.5 701 702 703 704 705 706 707 708 709 672 634 696 757 819 880 942 85003 065 578 640 702 763 825 887 948 009 071 584 646 708 770 831 893 954 016 077 590 652 714 776 837 899 960 022 083 597 658 720 782 844 905 967 028 089 603 665 726 788 850 911 973 034 095 609 671 733 794 856 917 979 040 101 615 677 739 800 862 924 985 046 107 621 683 745 807 868 930 991 052 114 628 689 751 813 874 936 997 058 120 710 126 132 138 144 150 156 163 169 175 181 711 712 713 714 715 716 717 718 719 187 248 309 370 431 491 552 612 673 193 254 315 376 437 497 558 618 679 199 260 321 382 443 503 564 625 685 205 266 327 388 449 509 570 631 691 211 272 333 394 455 516 576 637 697 217 278 339 400 461 522 582 643 703 224 285 345 406 467 528 688 649 709 230 291 352 412 473 534 594 655 715 236 297 358 418 479 540 600 661 721 242 303 364 425 485 546 606 667 727 720 733 739 745 751 757 763 769 775 781 788 721 722 723 724 725 726 727 728 729 794 854 914 974 86034 094 153 213 273 800 860 920 980 040 100 159 219 279 806 866 926 986 046 106 165 225 285 812 872 932 992 052 112 171 231 291 818 878 938 998 058 118 177 237 297 824 884 944 *004 064 124 183 243 303 830 890 950 *010 070 130 189 249 308 836 896 956 *016 076 136 195 255 314 842 902 962 *022 082 141 201 261 320 848 908 968 *028 088 147 207 267 326 730 332 338 344 350 356 362 368 374 380 386 731 732 733 734 735 736 737 738 739 392 451 610 670 629 688 747 806 864 398 457 516 576 635 694 753 812 870 404 ~4E3 522 581 641 700 759 817 876 410 469 528 587 646 705 764 823 882 415 475 534 593 652 711 770 829 888 421 481 540 599 658 717 776 835 894 427 487 546 605 664 723 782 841 900 433 493 552 611 670 729 788 847 906 439 499 558 617 676 735 794 853 911 445 504 564 623 682 74J 800 859 917 740 923 929 935 941 947 953 958 964 970 976 741 742 743 744 745 746 747 748 749 982 87040 099 157 216 274 332 390 448 988 046 105 163 221 280 338 396 454 994 052 111 169 227 286 344 402 460 999 058 116 175 233 291 349 408 466 *005 064 122 181 239 297 355 413 471 *011 070 128 186 245 303 361 419 477 *017 075 134 192 251 309 367 425 483 *023 081 140 198 256 315 373 431 489 *029 087 146 204 262 320 379 437 495 *035 093 151 210 268 326 384 442 500 750 506 512 518 523 529 535 541 547 552 558 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. I] 750 Logarithms of Numbers 800 15 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 750 87506 512 518 523 529 535 541 547 552 558 6 5 1 0.6 0.5 2 1.2 1.0 3 1.8 1.5 4 2.4 2.0 5 3.0 2.5 6 3.6 3.0 7 4.2 3.5 8 4.8 4.0 9 5.4 4.5 751 752 753 754 755 756 757 758 759 564 622 679 737 795 852 910 967 88024 570 628 685 743 800 858 915 973 030 576 633 691 749 806 864 921 978 036 581 639 697 754 812 869 927 984 041 587 645 703 760 818 875 933 990 047 593 651 708 766 823 881 938 996 053 599 656 714 772 829 887 944 *001 058 604 662 720 777 835 892 950 *007 064 610 668 726 783 841 898 955 *013 070 616 674 731 789 846 904 961 *018 076 760 081 087 093 098 104 110 116 121 127 133 761 762 763 764 765 766 767 768 769 138 195 252 309 366 423 480 536 593 144 201 258 315 372 429 485 542 598 150 207 264 321 377 434 491 547 604 156 213 270 (326> 161 218 275 332 389 446 502 559 615 167 224 281 338 395 451 508 564 621 173 230 287 343 400 457 513 570 627 178 235 292 349 406 463 519 576 632 184 241 298 355 412 468 525 581 638 190 247 304 360 417 474 530 587 643 440 497 553 610 770 649 655 660 666 672 677 683 689 694 700 771 772 773 774 775 776 777 778 779 705 762 818 874 930 986 89042 098 154 711 767 824 880 936 992 048 104 159 717 773 829 885 941 997 053 109 165 722 779 835 891 947 *003 059 115 170 728 784 840 897 953 *009 064 120 176 734 790 846 902 958 *014 070 126 182 739 795 852 908 964 *020 076 131 187 745 801 857 913 969 *025 081 137 193 750 807 863 919 975 *031 087 143 198 756 812 868 925 981 *037 092 148 204 780 209 215 221 226 232 237 243 248 254 260 781 782 783 784 785 786 787 788 789 265 321 376 432 487 542 597 653 708 271 326 382 437 492 548 603 658 713 276 332 387 443 498 553 609 664 719 282 337 393 448 504 559 614 669 724 287 343 398 454 509 564 620 675 730 293 348 404 459 515 570 625 680 735 298 354 409 465 520 575 631 686 741 304 360 415 470 526 581 636 691 746 310 365 421 476 531 586 642 697 752 315 371 426 481 537 592 647 702 757 790 763 768 774 779 785 790 796 801 807 812 791 792 793 794 795 796 797 798 799 818 873 927 982 90037 091 146 200 255 823 878 933 988 042 097 151 206 260 829 883 938 993 048 102 157 211 266 834 889 944 998 053 108 162 217 271 840 894 949 *004 059 113 168 222 276 845 900 955 *009 064 119 173 227 282 851 905 960 *015 069 124 179 233 287 856 911 966 *020 075 129 184 238 293 862 916 971 *026 080 135 189 244 298 867 922 977 *031 086 140 195 249 304 800 309 314 320 325 331 336 342 347 352 358 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 16 800 Logarithms of Numbers 850 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 800 90309 314 320 325 331 336 342 347 352 358 801 363 369 374 380 385 390 396 401 407 412 802 417 423 428 434 439 445 450 455 461 466 803 472 4tff 482 488 493 499 504 509 515 520 804 526 53li 536 542 547 553 558 563 569 574 805 580 585 590 596 601 607 612 617 623 628 806 634 639 644 650 655 660 666 671 677 682 807 687 693 698 703 709 714 720 725 730 736 808 741 747 752 757 763 768 773 779 784 789 809 795 800 806 811 816 '822 827 832 838 843 810 849 854 859 865 870 875 881 886 891 897 811 902 907 913 918 924 929 934 940 945 950 812 956 961 966 972 977 982 988 993 998 *004 813 91009 014 020 025 030 036 041 046 052 057 814 062 068 073 078 084 089 094 100 105 110 815 116 121 126 132 137 142 148 153 158 164 816 169 174 180 185 190 196 201 206 212 217 817 222 228 233 238 243 249 254 259 265 270 818 275 281 286 291 297 302 307 312 318 323 819 328 334 339 344 350 355 360 365 371 376 820 381 387 392 397 403 408 413 418 424 429 IX 61 821 434 440 445 450 455 461 466 471 477 482 5 822 487 492 498 503 508 514 519 524 529 535 1 0.6 0.5 823 540 545 551 556 561 566 572 577 582 587 2 1.2 1.0 824 593 598 603 609 614 619 624 630 635 640 3 1.8 1.5 825 645 651 656 661 666 672 677 682 687 693 4. 2.4 2.0 826 698 703 709 714 719 724 730 735 740 745 5 3.0 2.5 6 3.6 3.0 827 751 756 761 766 772 777 782 787 793 798 7 4.2 3.5 828 803 808 814 819 824 829 834 840 845 850 8 4.8 4.0 829 855 861 866 871 876 882 887 892 897 903 9 5.4 4.5 830 908 913 918 924 929 934 939 944 950 955 831 960 965 971 976 981 986 991 997 *002 *007 832 92012 018 023 028 033 038 044 049 054 059 833 065 070 075 080 085 091 096 101 106 111 834 117 122 127 132 137 143 148 153 158 163 835 169 174 179 184 189 195 200 205 210 215 836 221 226 231 236 241 247 252 257 262 267 837 273 278 283 288 293 298 304 309 314 319 838 324 330 335 340 345 350 355 361 366 371 839 376 381 387 392 397 402 407 412 418 423 840 428 433 438 443 449 454 459 464 469 474 841 480 485 490 495 500 505 511 516 521 526 842 531 536 542 547 552 557 562 567 J2 578 843 583 588 593 598 603 609 614 619 624 629 844 634 639 645 650 655 660 665 670 675 681 845 686 691 696 701 706 711 716 722 727 732 846 737 742 747 752 758 703 768 773 778 783 847 788 793 799 804 809 814 819 824 829 834 848 840 845 850 855 860 865 870 875 881 886 849 891 896 901 906 911 916 921 927 932 937 850 942 947 952 957 962 9G7 973 978 983 988 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 850 Logarithms of Numbers 900 17 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 850 92942 947 952 957 962 967 973 978 983 988 851 993 998 *003 *008 *013 *018 *024 *029 *034 *039 852 93044 049 054 059 064 069 075 080 085 090 853 095 100 105 110 115 120 125 131 136 141 854 146 151 156 161 166 171 176 181 186 192 855 197 202 207 212 217 222 227 232 237 242 856 247 252 258 263 268 273 278 283 288 293 857 298 303 308 313 318 323 328 334 339 344 858 349 354 359 364' 369 374 379 384 389 394 859 399 404 409 414 420 425 430 435 440 445 860 450 455 460 465 470 475 480 485 490 495 6C " 861 500 505 510 515 520 526 531 536 541 546 5 862 551 556 561 566 571 576 581 586 591 596 1 0.6 0.5 863 601 606 611 616 621 626 63 !., 636 641 646 2 1.2 1.0 864 651 656 661 666 671 676 682 687 692 697 3 1.8 1.5 49 A 9 H 865 702 707 712 717 722 727 732 737 742 747 -.T: it\J c ^09^ 866 752 757 762 767 772 777 782 787 792 797 cl O*U .>> 6 3.6 3.0 867 802 807 812 817 822 827 832 837 842 847 7 4.2 3.5 868 852 857 862 867 872 877 882 887 892 897 8 4.8 4.0 869 902 907 912 917 922 927 932 937 942 947 9 5.4 4.5 870 952 957 962 967 972 977 982 987 992 997 871 94002 007 012 017 022 027 032 037 042 047 872 052 057 062 067 072 077 082 086 091 096 873 101 106 111 116 121 126 131 136 141 146 874 151 156 161 166 171 176 181 186 191 196 875 201 206 211 216 221 226 231 236 240 245 876 250 255 260 265 270 275 280 285 290 295 877 300 305 310 315 320 325 330 335 340 345 878 349 354 359 364 369 374 379 384 389 394 879 399 404 409 414 419 424 429 433 438 443 880 448 453 458 463 468 473 478 483 488 493 881 498 503 507 512 517 522 527 532 537 542 4 882 547 552 557 562 567 571 576 581 586 591 1 0.4 883 596 601 606 611 616 621 626 630 '635 640 2 0.8 884 645 650 655 660 665 670 675 680 685 689 3 1.2 885 694 699 704 709 714 719 724 729 734 738 4 1.6 50 n 886 743 748 753 758 763 768 773 778 783 787 Z.U 6 2.4 887 792 797 802 807 812 817 822 827 832 836 7 2.8 888 841 846 851 856 861 866 871 876 880 885 8 3.2 889 890 895 900 905 910 915 919 924 929 934 9 3.6 890 939 944 949 954 959 963 968 973 978 983 891 988 993 998 *002 *007 *012 *017 *022 *027 *032 892 95036 041 046 051 056 061 066 071 075 080 893 085 090 095 100 105 109 114 119 124 129 894 134 139 143 148 153 158 163 168 173 177 895 182 187 192 197 202 207 211 216 221 226 896 231 236 240 245 250 255 260 265 270 274 897 279 284 289 294 299 303 308 313 318 323 898 328 332 337 342 347 352 357 361 366 371 899 376 381 386 390 395 400 405 410 415 419 900 424 429 434 439 444 448 453 458 463 468 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 18 900 Logarithms of Numbers 950 [1 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 900 95424 429 434 439 444 448 453 458 463 468 5 4 1 US 0.4 2 1.0 0.8 3 1.5 1.2 4 2.0 1.6 5 2.5 2.0 6 3.0 2.4 7 3.5 2.8 8 4.0 3.2 9 4.5 3.6 901 902 903 904 905 906 907 908 909 472 521 569 617 665 713 761 809 856 477 525 574 622 670" 718 766 813 861 482 530 578 626 674 722 770 818 866 487 535 583 631 679 727 775 823 871 492 540 588 636 684 732 780 828 875 497 545 593 641 689 737 785 832 880 501 550 598 646 694 742 789 837 885 506 554 602 650 698 746 794 842 890 511 559 607 655 703 751 799 847 895 516 564 612 660 708 756 804 852 899 910 904 909 914 918 923 928 933 938 942 947 911 912 913 914 915 916 917 918 919 952 999 96047 095 142 190 237 284 332 957 *004 052 099 147 194 242 289 336 961 *009 057 104 152 199 246 294 341 966 *014 061 109 156 204 251 298 346 971 *019 066 114 161 209 256 303 350 976 *023 071 118 1"66 213 261 308 355 980 *028 076 123 171 218 265 313 360 985 *033 080 128 175 223 270 317 365 990 *038 085 133 180 227 275 322 369 995 *042 090 137 185 232 280 327 374 920 379 384 388 393 398 402 407 412 417 421 921 922 923 924 925 926 927 928 929 426 473 520 567 614 661 708 755 802 431 478 525 572 619 666 713 759 806 435 483 530 577 624 670 717 764 811 440 487 534 581 628 675 722 769 816 445 492 539 586 633 680 727 774 820 450 497 544 591 638 685 731 778 825 454 501 548 595 642 689 736 783 830 459 506 553 600 0.47 464 511 558 605 652 69^ 745 792 839 468 515 562 609 656 703 750 797 844 654 741 788 834 930 848 853 858 862 867 872 876 881 886 890 931 932 933 934 935 936 937 938 939 895 942 988 97035 081 128 174 220 267 900 946 993 039 086 132 179 225 271 904 951 997 044 090 137 183 230 276 909 956 *002 049 095 142 188 234 280 914 960 *007 053 100 146 192 239 285 918 965 *011 058 104 151 197 243 290 923 970 *016 063 109 155 202 248 294 928 974 *021 067 114 160 206 253 299 932 979 *025 072 118 165 211 257 304 937 984 *030 077 123 169 216 262 308 940 313 317 322 327 331 336 340 345 350 354 941 942 943 944 945 946 947 948 949 359 405 451 497 543 589 635 681 727 364 410 456 502 548 594 640 685 731 368 414 460 506 552 598 644 690 736 373 419 465 511 557 603 649 695 740 377 424 470 516 562 607 653 699 745 382 428 474 520 566 612 658 704 749 387 433 479 525 571 617 663 708 754 391 437 483 529 575 621 667 713 759 396 442 488 534 580 626 672 717 763 400 447 493 539 585 630 676 722 768 950 772 777 782 786 791 795 800 804 809 813 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 950 Logarithms of Numbers 1000 19 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 950 97772 777 782 786 791 795 800 804 809 813 951 818 823 827 832 836 841 845 850 855 859 952 864 868 873 877 88^ 886 ~891 896 900 905 953 909 914 918 923 928 932 937 941 946 950 954 955 959 964 968 973 978 982 987 991 996 955 98000 005 009 014 019 023 028 032 037 041 956 046 050 055 059 064 068 073 078 082 087 957 091 096 100 105 109 114 118 123 127 132 958 137 141 146 150 155 159 164 168 173 177 959 182 186 191 195 200 204 209 214 218 223 960 227 232 236 241 245 250 254 259 263 268 961 272 277 281 286 290 295 299 304 308 313 962 318 322 327 331 336 340 345 349 354 358 963 363 367 372 376 381 385 390 394 399 403 964 408 412 417 421 426 430 435 439 444 448 965 453 457 462 466 471 475 480 484 489 493 966 498 502 507 511 516 620 525 529 534 538 967 543 547 552 556 561 565 570 574 579 583 968 588 592 597 601 605 610 614 619 623 628 969 632 637 641 646 650 655 659 664 668 673 970 677 682 686 691 695 700 704 709 713 717 5. A 971 722 726 731 735 740 744 749 753 758 762 4 972 767 771 776 780 784 789 793 798 802 807 1 0.5 0.4 973 811 816 820 825 829 834 838 843 847 851 2 1.0 0.8 974 856 860 865 869 874 878 883 887 892 896 3 1.5 1.2 490 1 fi 975 900 905 909 914 918 923 927 932 936 941 &\j i ,\> 5 2.5 2.0 976 945 949 954 958 963 967 972 976 981 985 6 3!o 2!4 977 989 994 998 *003 *007 *012 *016 *021 *025 *029 7 3.5 2.8 978 99034 038 043 047 052 056 061 065 069 074 8 4.0 3.2 979 078 083 087 092 096 100 105 109 114 118 9 4.6 3.6 980 123 127 131 136 140 145 149 154 158 162 981 167 171 176 180 185 189 193 198 202 207 982 211 216 220 224 229 233 238 242 247 251 983 255 260 264 269 273 277 282 286 291 295 984 300 304 308 313 317 322 326 330 335 339 985 344 348 352 357 361 366 370 374 379 383 986 388 392 396 401 405 410 414 419 423 427 987 432 436 441 445 449 454 458 463 467 471 988 476 480 484 489 493 498 502 506 511 515 989 520 524 528 533 537 542 546 550 555 559 990 564 568 572 577 681 585 590 594 599 603 991 607 612 616 621 625 629 634 638 642 647 992 651 656 660 664 669 673 677 682 686 691 993 695 699 704 708 712 717 721 726 730 734 994 739 743 747 752 756 760 765 769 774 778 995 782 787 791 795 800 804 808 813 817 822 996 826 830 835 839 843 848 852 856 861 865 997 870 874 878 883 887 891 896 900 904 909 998 913 917 922 926 930 935 939 944 948 952 999 957 961 965 970 974 978 983 987 991 996 1000 00000 004 009 013 017 022 026 030 035 039 N. 1 2 3 4 5 6 7 8 9 Prop. Pts. 20 Table la Condensed Logarithms and Antilogarithms 1* CONDENSED LOGARITHMS TO FIFTEEN DECIMAL PLACES [The first digits of n are given in the first row at the top; the last digit of n in the left-hand column. The first column of logarithms are those of 1, 2, 3, , 9. The remaining columns give log (1 + x), where x = (0.1)* times 1, 2, , 9.] First Digit of n 1. 1.0 1.00 Log n First Digits of log n .0 .00 00000 00000 00000 30102 99956 63981 47712 12547 19662 60205 99913 27962 69897 00043 36019 77815 12503 83644 84509 80400 14257 90308 99869 91944 95424 25094 39325 04139 26851 58225 07918 12460 47625 11394 33523 06837 14612 80356 78238 17609 12590 55681 204119982655925 23044 89213 78274 25527 25051 03306 27875 36009 52829 0432 13737 82643 08600171761918 1283 72247 05172 1703 33392 98780 21189299069938 2530 58652 64770 2938 37776 85210 3342 37554 86950 3742 64979 40624 (continuation) 1.000 1.0000 1.00000 1.000000 1.0000000 1.00000000 .000 .0000 .00000 .000000 .0000000 .00000000 1 2 3 4 5 6 7 8 9 04 34272 76863 0868502 11649 13 02688 05227 17 36830 58465 21 70929 72230 26 04985 47390 30 38997 84812 34 72966 85364 39 06892 49910 04342923104 86858 02780 1 30286 39028 1 73714 31850 2 17141 81245 26056887215 3 03995 49761 3 47421 68884 3 90847 44584 04342 94265 08685 88095 1302881491 17371 74453 21714 66981 26057 59074 30400 50733 34743 41958 39086 32748 0434 29446 0868 58888 1302 88325 1737 17758 2171 47187 260576611 304006031 3474 35447 3908 64858 043 42945 086 85890 130 28834 173 71779 217 14724 260 57668 304 00613 347 43557 390 86502 04 34294 08 68589 13 02883 17 37178 21 71472 26 05767 30 40061 34 74356 39 08650 [For x < .00000001, log (1 + x) = x-M, to within 3 in the 17th place, where M = 0.43429448 . Hence the last column gives multiples of M except for the decimal place. All the columns that would follow have the same significant digits displaced each time one place.] CONDENSED ANTILOGARITHMS TO TEN DECIMAL PLACES [The first digits of n are given in the first row at the top; n = (0.1)* x; x = 1, 2, 3, , 9 are given in the left-hand column, second row at the top.] The first digits in 10" are given in the X n = 0.1* O.Ola; O.OOlx O.OOOlx (O.I) 6 * (0.1) 6 z (0.1)'* 10" 1. 1.0 1.00 1.000 1.0000 1.00000 1 1.2589254118 02329 29923 0230 52381 023 02850 02 30261 23026 02303 2 1.58489 31925 04712 85481 0461 57903 046 06231 04 60528 46052 04605 3 1.99526 23150 07151 93052 0693 16689 069 10142 06 90799 69078 06908 4 2.51188 64315 09647 81961 0925 28861 092 14583 09 21076 92104 09210 5 3.16227 76602 12201 84543 115794543 115 19555 11 51359 1 15130 11513 6 3.98107 17055 14815 36215 1391 13857 138 25058 13 81646 1 38156 13816 7 5.0118723363 17489 75549 1624 86929 161 31092 16 11939 1 61182 16118 8 6.30957 34448 20226 44346 1859 13881 184 37657 18 42238 1 84209 18421 9 7.94328 23472 23026 87708 2093 94837 207 44753 20 72541 2 07235 20723 [For n < 0.000001, 10" = 1 + n- (l/M) to within 3 in the 12th decimal place, where (l/M) = 2.302585 . Hence the last column gives multiples of (l/M) except for the decimal place. All the columns that would follow contain the same significant digits displaced one place for each new column.] TABLE E ACTUAL VALUES OF THE TRIGONOMETRIC FUNCTIONS TO FIVE DECIMAL PLACES Trigonometric Functions and Their Inverses Thus y = sin x gives x = arc sin y 22 Values of Trigonometric Functions [II / Sin Tan Ctn Cos / Sin Tan Ctn Cos .00000 .00000 1.0000 60 .01745 .01746 57.290 .99985 60 1 029 029 3437.7 000 59 1 774 775 56.351 984 59 2 058 a a 058 1718.9 000 58 2 803 804 55.442 984 58 3 08J- ) l l 087 1145.9 000 5'. 3 832 833 54.561 983 57 4 lie: VJ 116 859.44 000 56 4 862 862 53.709 983 56 5 .00145- Iflbl46 687.55 1.0000 55 5 .01891 .01891 52.882 .99982 55 6 175 175 572.96 000 54 6 920 920 52.081 982 54 7 204 204 491.11 000 53 7 949 949 51.303 981 53 8 233 i 2*3 429.72 000 52 8 .01978 .01978 50.549 980 52 9 262 ^262 381.97 000 51 9 .02007 .02007 49.816 980 51 10 .00291 >.\)0291 343.77 1.0000 50 10 .02036 .02036 49.104 .99979 50 11 320 320 312.52 .99999 49 11 065 066 48.412 979 49 12 349 349 286.48 999 48 12 094 095 47.740 978 48 13 378 378 264.44 999 47 13 123 124 47.085 977 47 14 407 407 245.55 999 46 14 152 153 46.449 977 46 15 .00436 .00436 229.18 .99999 45 15 .02181 .02182 45.829 .99976 45 16 465 465 214.86 999 44 16 211 211 45.226 976 44 17 495 495 202.22 999 43 17 240 240 44.639 975 43 18 524 524 190.98 999 42 18 269 269 44.066 974 42 19 553 553 180.93 998 41 19 298 298 43.508 974 41 20 .00582 .00582 171.89 .99998 40 20 .02327 .02328 42.964 .99973 40 21 611 611 163.70 998 39 21 356 357 42.433 972 39 22 640 640 156.26 998 38 22 385 386 41.916 972 38 23 669 669 149.47 998 37 23 414 415 41.411 971 37 24 698 698 143.24 998 36 24 443 444 40.917 970 36 25 .00727 .00727 137.51 .99997 35 25 .02472 .02473 40.436 .99969 35 26 756 756 132.22 997 34 26 501 502 39.965 969 34 27 785 785 127.32 997 33 27 530 531 39.506 968 33 28 814 815 122.77 997 32 28 560 560 39.057 967 32 29 844 844 118.54 996 31 29 589 589 38.618 966 31 30 .00873 .00873 114.59 .99996 30 30 .02618 .02619 38.188 .99966 30 31 902 902 110.89 996 29 31 647 648 37.769 965 29 32 931 931 107.43 996 28 32 676 677 37.358 964 28 33 960 960 104.17 995 27 33 705 706 36.956 963 27 34 .00989 .00989 101.11 995 26 34 734 735 36.563 963 26 35 .01018 .01018 98.218 .99995 25 35 .02763 .02764 36.178 .99962 25 36 047 047 95.489 995 24 36 792 793 35.801 961 24 37 076 076 92.908 994 23 37 821 822 35.431 960 23 38 105 105 90.463 994 22 38 850 851 35.070 959 22 39 134 135 88.144 994 21 39 879 881 34.715 959 21 40 .01164 .01164 85.940 .99993 20 40 .02908 .02910 34.368 .99958 20 41 193 193 83.844 993 19 41 938 939 34.027 957 19 42 222 222 81.847 993 18 42 967 968 33.694 956 18 43 251 251 79.943 992 17 43 .02996 .02997 33.366 955 17 44 280 280 78.126 992 16 44 .03025 .03026 33.045 954 16 45 .01309 .01309 76.390 .99991 15 45 .03054 .03055 32.730 .99953 15 46 338 338 74.729 991 14 46 083 084 32.421 952 14 47 367 367 73.139 991 13 47 112 114 32.118 952 13 48 396 396 71.615 990 12 48 141 143 31.821 951 12 49 425 425 70.153 990 11 49 170 172 31.528 950 11 50 .01454 .01455 68.750 .99989 10 50 .03199 .03201 31.242 .99949 10 51 483 484 67.402 989 9 51 228 230 30.960 948 9 52 513 513 66.105 989 8 52 257 259 30.683 947 8 53 542 542 64.858 988 7 53 286 288 30.412 946 7 54 571 571 63.657 988 6 54 316 317 30.145 945 6 55 .01600 .01600 62.499 .99987 5 55 .03345 .03346 29.882 .99944 5 56 629 629 61.383 987 4 56 374 376 29.624 943 4 57 658 658 60.306 986 3 57 403 405 29.371 942 3 58 687 687 59.266 986 2 58 432 434 29.122 941 2 59 716 716 58.261 985 1 59 461 463 28.877 940 1 60 .01745 .01746 57.290 .99985 60 .03490 .03492 28.636 .99939 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 89 88 C II] 2 Values of Trigonometric Functions 3 e / Sin Tan Ctn Cos ' Sin Tan Ctn Cos 03490 .03492 28.636 .99939 60 .05234 .05241 19.081 .99863 60 1 519 521 .399 938 59 1 263 270 18.976 861 59 2 548 550 28.166 937 58 2 292 299 .871 860 58 3 577 579 27.937 936 57 3 321 328 .768 858 57 4 606 609 .712 935 56 4 350 357 .666 857 56 5 03635 .03638 27.490 .99934 55 5 .05379 .05387 18.564 .99855 55 6 664 667 .271 933 54 6 408 416 .464 854 54 7 693 696 27.057 932 53 7 437 445 .366 852 53 8 723 725 26.845 931 52 8 466 474 .268 851 52 9 752 754 .637 930 51 9 495 503 .171 849 51 10 03781 .03783 26.432 .99929 50 10 .05524 .05533 18.075 .99847 50 11 810 812 .230 927 49 11 553 562 17.980 846 49 12 839 842 26.031 926 48 12 582 591 .886 844 48 13 868 871 25.835 925 47 13 611 620 .793 842 47 14 897 900 .642 924 46 14 640 649 .702 841 46 15 .03926 .03929 25.452 .99923 45 15 .05669 .05678 17.611 .99839 45 16 955 958 .264 922 44 16 698 708 .521 838 44 17 .03984 .03987 25.080 921 43 17 727 737 .431 836 43 18 .04013 .04016 24.898 919 42 18 756 766 .343 834 42 19 042 046 .719 918 41 19 785 795 .256 833 41 20 .04071 .04075 24.542 .99917 40 20 .05814 .05824 17.169 .99831 40 21 100 104 .368 916 39 21 844 854 17.084 829 39 22 129 133 .196 915 38 22 873 883 16.999 827 38 23 159 162 24.026 913 37 23 902 912 .915 826 37 24 188 191 23.859 912 36 24 931 941 .832 824 36 25 .04217 .04220 23.695 .99911 35 25 .05960 .05970 16.750 .99822 35 26 246 250 .532 910 34 26 .05989 .05999 .668 821 34 27 275 279 .372 909 33 27 .06018 .06029 .587 819 33 28 304 308 .214 907 32 28 047 058 .507 817 32 29 333 337 23.058 906 31 29 076 087 .428 815 31 30 .04362 .04366 22.904 .99905 30 30 .06105 .06116 16.350 .99813 30 31 391 395 .752 904 29 31 134 145 .272 812 29 32 420 424 .602 902 28 32 163 - 175 .195 810 28 33 449 454 .454 901 27 33 192 204 .119 808 27 34 478 483 .308 900 26 34 221 233 16.043 806 26 35 .04507 .04512 22.164 .99898 25 35 '.002i>lT "!06262 15.969 .99804 25 36 536 541 22.022 897 24 36 279 291 .895 803 24 37 565 670 21.881 896 23 37 308 321 .821 801 23 38 594 599 .743 894 22 38 337 350 .748 799 22 39 623 628 .606 893 21 39 366 379 .676 797 21 40 .04653 .04658 21.470 .99892 20 40 .06395 .06408 15.605 .99795 20 41 682 687 .337 890 19 41 424 438 .534 793 19 42 711 716 .205 889 18 42 453 467 .464 792 18 43 740 745 21.075 888 17 43 482 496 .394 790 17 44 769 774 20.946 886 16 44 511 525 .325 788 16 45 .04798 .04803 20.819 .99885 15 45 .06540 .06554 15.257 .99786 15 46 827 833 .693 883 14 46 569 584 .189 784 14 47 856 862 .569 882 13 47 598 613 .122 782 13 48 885 891 .446 881 12 48 627 642 15.056 780 12 49 914 920 .325 879 11 49 656 671 14.990 778 11 50 .04943 .04949 20.206 .99878 10 50 .06685 .06700 14.924 .99776 10 51 .04972 .04978 20.087 876 9 51 714 730 .860 774 9 52 .05001 .05007 19.970 875 8 52 743 759 .795 772 8 53 030 037 .855 873 7 53 773 788 .732 770 7 54 059 066 .740 872 6 54 802 817 .669 768 6 55 .05088 .05095 19.627 .99870 5 55 .06831 .06847 14.606 .99766 5 56 117 124 .516 869 4 56 860 876 .544 764 4 57 146 153 .405 867 3 57 889 905 .482 762 3 58 175 182 .296 866 2 58 918 934 .421 76U 2 59 205 212 .188 864 1 59 947 963 .361 758 1 60 .05234 .05241 19.081 .99863 60 .06976 .06993 14.301 .99756 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 87 86 C '24 4 Values of Trigonometric Functions 5 C [II 1 Sin Tan Ctn Cos i Sin Tan Ctn Cos .06976 .06993 14.301 .99756 60 .08716 .08749 11.430 .99619 60 1 .07005 .07022 .241 754 59 1 745 778 .392 617 59 2 034 051 .182 752 58 2 774 807 .354 614 58 3 063 080 .124 750 57 3 803 837 .316 612 57 4 092 110 .065 748 56 4 831 866 .279 609 56 5 .07121 .07139 14.008 .99746 55 5 .08860 .08895 11.242 .99607 55 6 150 168 13.951 744 54 6 889 925 .205 604 54 7 179 197 .894 742 53 7 918 954 .168 602 53 8 208 227 .838 740 52 8 947 .08983 .132 599 52 9 237 256 .782 738 51 9 .08976 .09013 .095 596 51 10 .07266 .07285 13.727 .99736 50 10 .09005 .09042 11.059 .99594 50 11 295 314 .672 734 49 11 034 071 11.024 591 49 12 324 344 .617 731 48 12 063 101 10.988 588 48 13 353 373 .563 729 47 13 092 130 .953 586 47 14 382 402 .510 111 46 14 121 159 .918 583 46 15 .07411 .07431 13.457 .99725 45 15 .09150 .09189 10.883 .99580 45 16 440 461 .404 723 44 16 179 218 .848 578 44 17 469 490 .352 721 43 17 208 247 .814 575 43 18 498 519 .300 719 42 18 237 111 .780 572 42 19 527 548 .248 716 41 19 266 306 .746 570 41 20 .07556 .07578 13.197 .99714 40 20 .09295 .09335 10.712 .99567 40 21 585 607 .146 712 39 21 324 365 .678 564 39 22 614 636 .096 710 38 22 353 394 .645 562 38 23 643 665 13.046 708 37 23 382 423 .612 559 37 24 672 695 12.996 705 36 24 411 453 .579 556 36 25 .07701 .07724 12.947 .99703 35 25 .09440 .09482 10.546 .99553 35 26 730 753 .898 701 34 26 469 511 .514 551 34 27 759 782 .850 699 33 27 498 541 .481 548 33 28 788 812 .801 696 32 28 527 570 .449 545 32 29 817 841 .754 694 31 29 556 600 .417 542 31 30 .07846 .07870 12.706 .99692 30 30 .09585 .09629 10.385 .99540 30 31 875 899 .659 689 29 31 614 658 .354 537 29 32 904 929 .612 687 28 32 642 688 .322 534 28 33 933 958 .566 685 27 33 671 717 .291 531 27 34 962 .07987 .520 683 26 34 700 746 .260 528 26 35 .07991 .08017 12.474 .99680 25 35 .09729 .09776 10.229 .99526 25 36 .08020 046 .429 678 24 36 758 805 .199 523 24 37 049 075 .384 676 23 37 787 834 .168 520 23 38 078 104 .339 673 22 38 816 864 .138 517 22 39 107 134 .295 671 21 39 845 893 .108 514 21 40 .08136 .08163 12.251 .99668 20 40 .09874 .09923 10.078 .99511 20 41 165 192 .207 666 19 41 903 952 .048 508 19 42 194 221 .163 664 18 42 932 .09981 10.019 506 18 43 223 251 .120 661 17 43 961 .10011 9.9893 503 17 44 252 280 .077 659 16 44 .09990 040 .9601 500 16 45 .08281 .08309 12.035 .99657 15 45 .10019 .10069 9.9310 .99497 15 46 310 339 11.992 654 14 46 048 099 .9021 494 14 47 339 368 .950 652 13 47 077 128 .8734 491 13 48 368 397 .909 649 12 48 106 158 .8448 488 12 49 397 427 .867 647 11 49 135 187 .8164 485 11 50 .08426 .08456 11.826 .99644 10 50 .10164 .10216 9.7882 .99482 10 51 455 485 .785 642 9 51 192 246 .7601 479 9 52 484 514 .745 639 8 52 221 275 .7322 476 8 53 513 544 .705 637 7 53 250 305 .7044 473 7 54 542 573 .664 635 6 54 279 334 .6768 470 6 55 .08571 .08602 11.625 .99632 5 55 .10308 .10363 9.6493 .99467 5 56 600 632 .585 630 4 56 337 393 .6220 464 4 57 629 661 .546 627 3 57 366 422 .5949 461 3 58 658 690 .507 625 2 58 395 452 .5679 458 2 59 687 720 .468 622 1 59 424 481 .5411 455 1 60 .08716 .08749 11.430 .99619 60 .10453 .10510 9.5144 .99452 Cos Ctn Tan Sin ' Cos Ctn Tan Sin / 85 84 C II] 6 Values of Trigonometric Functions T 25 / Sin Tan Ctn Cos / Sin Tan Ctn Cos 10453 .10510 9.5144 .99452 60 .12187 .12278 8.1443 .99255 60 1 482 540 .4878 449 59 1 216 308 .1248 251 59 2 511 569 .4614 446 58 2 245 338 .1054 248 58 3 540 599 .4352 443 57 3 274 367 .0860 244 57 4 569 628 .4090 440 56 4 302 397 .0667 240 56 5 10597 .10657 9.3831 .99437 55 5 .12331 .12426 8.0476 .99237 55 6~ 626 687 .3572 434 54 6 360 456 .0285 233 54 7 655 716 .3315 431 53 7 389 485 8.0095 230 53 8 684 746 .3060 428 52 8 418 515 7.9906 226 52 9 713 775 .2806 424 51 9 447 544 .9718 222 51 10 10742 .10805 9.2553 .99421 50 10 .12476 .12574 7.9530 .99219 50 11 771 834 .2302 418 49 11 504 603 .9344 215 49 12 800 863 .2052 415 48 12 533 633 .9158 211 48 13 829 893 .1803 412 47 13 562 662 .8973 208 47 14 858 922 .1555 409 46 14 591 692 .8789 204 46 15 .10887 .10952 9.1309 .99406 45 15 .12620 .12722 7.8606 .99200 45 16 916 .10981 .1065 402 44 16 649 751 .8424 197 44 17 945 .11011 .0821 399 43 17 678 781 .8243 193 43 18 .10973 040 .0579 396 42 18 706 810 .8062 189 42 19 .11002 070 .0338 393 41 19 735 840 .7882 186 41 20 .11031 .11099 9.0098 .99390 40 20 .12764 .12869 7.7704 .99182 40 21 060 128 8.9860 386 39 21 793 899 .7525 178 39 22 089 158 .9623 383 38 22 822 929 .7348 175 38 23 118 187 .9387 380 37 23 851 958 .7171 171 37 24 147 217 .9152 377 36 24 880 .12988 .6996 167 36 25 .11176 .11246 8.8919 .99374 35 25 .12908 .13017 7.6821 .99163 35 26 205 276 .8686 370 34 26 937 047 .6647 160 34 27 ^-2tt 305 .8455 367 33 27 966 076 .6473 156 33 28 263 335 .8225 364 32 28 .12995 106 .6301 152 32 29 291 364 .7996 360 31 29 .13024 136 .6129 148 31 30 .11320 .11394 8.7769 .99357 30 30 .13053 .13165 7.5958 .99144 30 31 349 423 .7542 354 29 31 081 195 .5787 141 29 32 378 452 .7317 351 28 32 110 224 .5618 137 28 33 407 482 .7093 347 27 33 139 254 .5449 133 27 34 436 511 .6870 344 26 34 168 284 .5281 129 26 35 .11465 .11541 8.6648 .99341 25 35 .13197 .13313 7.5113 .99125 25 36 494 570 .6427 337 24 36 226 343 .4947 122 24 37 523 600 .6208 334 23 37 254 372 .4781 118 23 38 552 629 .5989 331 22 38 283 402 .4615 114 22 39 580 659 .5772 327 21 39 312 432 .4451 110 21 40 .11609 .11688 8.5555 .99324 20 40 .13341 .13461 7.4287 .99106 20 41 638 718 .5340 320 19 41 370 491 .4124 102 19 42 667 747 .5126 317 18 42 399 521 .3962 098 18 43 696 777 .4913 314 17 43 427 550 .3800 094 17 44 725 806 .4701 310 16 44 456 580 .3639 091 16 45 .11754 .11836 8.4490 .99307 15 45 .13485 .13609 7.3479 .99087 15 46 783 865 .4280 303 14 46 514 639 .3319 083 14 47 812 895 .4071 300 13 47 543 669 .3160 079 13 48 840 924 .3863 297 12 48 572 698 .3002 075 12 49 869 954 .3656 293 11 49 600 728 .2844 071 11 50 .11898 .11983 8.3450 .99290 10 50 .13629 .13758 7.2687 .99067 10 51 927 .12013 .3245 286 9 51 658 787 .2531 063 9 52 956 042 .3041 283 8 52 687 817 .2375 059 8 53 .11985 072 .2838 279 7 53 716 846 .2220 055 7 54 .12014 101 .2636 276 6 54 744 876 .2066 051 6 55 .12043 .12131 8.2434 .99272 5 55 .13773 .13906 7.1912 .99047 5 56 071 160 .2234 269 4 56 802 935 .1759 043 4 57 100 190 .2035 265 3 57 831 965 .1607 039 3 58 129 219 .1837 262 2 58 860 .13995 .1455 035 2 59 158 249 .1640 258 1 59 889 .14024 .1304 031 1 60 .12187 .12278 8.1443 .99255 60 .13917 .14054 7.1154 .99027 Cos Ctn Tan Sin / Cos Ctn Tan Sin i 83 C 82 C 26 8 Values of Trigonometric Functions 9 C [II / Sin Tan Ctn Cos / Sin Tan Ctn Cos .13917 .14054 7.1154 .99027 60 .15643 .15838 6.3138 .98769 60 1 946 084 .1004 023 59 1 672 868 .3019 764 59 2 .13975 113 .0855 019 58 2 701 898 .2901 760 58 3 .14004 143 .0706 015 57 3 730 928 .2783 755 57 4 033 173 .0558 Oil 56 4 758 958 .2666 751 56 5 .14061 .14202 7.0410 .99006 55 5 .15787 .15988 6.2549 .98746 55 6 090 232 .0264 .99002 54 6 816 .16017 .2432 741 54 7 119 262 7.0117 .98998 53 7 845 047 .2316 737 53 8 148 291 6.9972 994 52 8 873 077 .2200 732 52 9 177 321 .9827 990 51 9 902 107 .2085 728 51 10 .14205 .14351 6.9682 .98986 50 10 .15931 .16137 6.1970 .98723 50 11 234 381 .9538 982 49 11 959 167 .1856 718 49 12 263 410 .9395 978 48 12 .15988 196 .1742 714 48 13 292 440 .9252 973 47 13 .16017 22C .1628 709 47 14 320 470 .9110 969 46 14 046 256 .1515 704 46 15 .14349 .14499 6.8969 .98965 45 15 .16074 .16286 6.1402 .98700 45 16 378 529 .8828 961 44 16 103 316 .1290 695 44 17 407 559 .8687 957 43 17 132 346 .1178 690 43 18 436 588 .8548 953 42 18 160 376 .1066 686 42 19 464 618 .8408 948 41 19 189 405 .0955 681 41 20 .14493 .14648 6.8269 .98944 40 20 .16218 .16435 6.0844 .98676 40 21 522 678 .8131 940 39 21 246 465 .0734 671 39 22 551 707 .7994 936 38 22 275 495 .0624 667 38 23 580 737 .7856 931 37 23 304 525 .0514 662 37 24 608 767 .7720 927 36 24 333 555 .0405 657 36 25 .14637 .14796 6.7584 .98923 35 25 .16361 .16585 6.0296 .98652 35 26 666 826 .7448 919 34 26 390 615 .0188 648 34 27 695 856 .7313 914 33 27 419 645 6.0080 643 33 28 723 886 .7179 910 32 28 447 674 5.9972 638 32 29 752 915 .7045 906 31 29 476 704 .9865 633 31 30 .14781 .14945 6.6912 .98902 30 30 .16505 .16734 5.9758 .98629 30 31 810 .14975 .6779 897 29 31 533 764 .9651 624 29 32 838 .15005 .6646 893 28 32 562 794 .9545 619 28 33 867 034 .6514 889 27 33 591 824 .9439 614 27 34 896 064 .6383 884 26 34 620 854 .9333 609 26 35 .14925 .15094 6.6252 .98880 25 35 .16648 .16884 5.9228 .98604 25 36 954 124 .6122 876 24 36 677 914 .9124 600 24 37 .14982 153 .5992 871 23 37 706 944 .9019 595 23 38 .15011 183 .5863 867 22 38 734 .16974 .8915 590 22 39 040 213 .5734 863 21 39 763 .17004 .8811 585 21 40 .15069 .15243 6.5606 .98858 20 40 .16792 .17033 5.8708 .98580 20 41 097 272 .5478 854 19 41 820 063 .8605 575 19 42 126 302 .5350 849 18 42 849 093 .8502 570 18 43 155 332 .5223 845 17 43 878 123 .8400 565 17 44 184 362 .5097 841 16 44 906 153 .8298 561 16 45 .15212 .15391 6.4971 .98836 15 45 .16935 .17183 5.8197 .98556 15 46 241 421 .4846 832 14 46 964 213 .8095 551 14 47 270 451 .4721 827 13 47 .16992 243 .7994 546 13 48 299 481 .4596 823 12 48 .17021 273 .7894 541 12 49 327 511 .4472 818 11 49 050 303 .7794 536 11 50 .15356 .15540 6.4348 .98814 10 50 .17078 .17333 5.7694 .98531 10 51 385 570 .4225 809 9 51 107 363 .7594 526 9 52 414 600 .4103 805 8 52 136 393 .7495 521 8 53 442 630 .3980 800 7 53 164 423 .7396 516 7 54 471 660 .3859 796 6 54 193 453 .7297 511 6 55 .15500 .15689 6.3737 .98791 5 55 .17222 .17483 5.7199 .98506 5 56 529 719 .3617 787 4 56 250 513 .7101 501 4 57 557 749 .3496 782 3 57 279 543 .7004 496 3 58 586 779 .3376 778 2 58 308 573 .6906 491 2 59 615 809 .3257 773 1 59 336 603 .6809 486 1 60 .15643 .15838 6.3138 .98769 60 .17365 .17633 5.6713 .98481 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 81 C 80 C II] 10 Values of Trigonometric Functions 11' 27 1 Sin Tan Ctn Cos / Sin Tan Ctn Cos .17365 .17633 5.6713 .98481 60 .19081 .19438 5.1446 .98163 60 1 393 663 .6617 476 59 1 109 468 .1366 157 59 2 422 693 .6521 471 58 2 138 498 .1286 152 58 3 451 723 .6425 466 57 3 167 529 .1207 146 57 4 479 753 .6329 461 56 4 195 559 .1128 140 56 5 .17508 .17783 5.6234 .98455 55 5 .19224 .19589 5.1049 .98135 55 6 537 813 .6140 450 54 6 252 619 .0970 129 54 7 565 843 .6045 445 53 7 281 649 .0892 124 53 8 594 873 .5951 440 52 8 309 680 .0814 118 52 9 623 903 .5857 435 51 9 338 710 .0736 112 51 10 .17651 .17933 5.5764 .98430 50 10 .19366 .19740 5.0658 .98107 50 11 680 963 .5671 425 49 11 395 770 .0581 101 49 12 708 .17993 .5578 420 48 12 423 801 .0504 096 48 13 737 .18023 .5485 414 47 13 452 831 .0427 090 47 14 766 053 .5393 409 46 14 481 861 .0350 084 46 15 .17794 .18083 5.5301 .98404 45 15 .19509 .19891 5.0273 .98079 45 16 823 113 .5209 399 44 16 538 921 .0197 073 44 17 852 143 .5118 394 43 17 566 952 .0121 067 43 18 880 173 .5026 389 42 18 595 .19982 5.0045 061 42 19 909 203 .4936 383 41 19 623 .20012 4.9969 056 41 20 .17937 .18233 5.4845 .98378 40 20 .19652 .20042 4.9894 .98050 40 21 966 263 .4755 373 39 21 680 073 .9819 044 39 22 .17995 293 .4665 368 38 22 709 103 .9744 039 38 23 .18023 323 .4575 362 37 23 737 133 .9669 033 37 24 052 353 .4486 357 36 24 766 164 .9594 027 36 25 .18081 .18384 5.4397 .98352 35 25 .19794 .20194 4.9520 .98021 35 26 109 414 .4308 347 34 26 823 224 .9446 016 34 27 138 444 .4219 341 33 27 851 254 .9372 010 33 28 166 474 .4131 336 32 28 880 285 .9298 .98004 32 29 195 504 .4043 331 31 29 908 315 .9225 .97998 31 30 .18224 .18534 5.3955 .98325 30 30 .19937 .20345 4.9152 .97992 30 31 252 564 .3868 320 29 31 965 376 .9078 987 29 32 281 594 .3781 315 28 32 .19994 406 .9006 981 28 33 309 624 .3694 310 27 33 .20022 436 .8933 975 27 34 338 654 .3607 304 26 34 051 466 .8860 969 26 35 .18367 .18684 5.3521 .98299 25 35 .20079 .20497 4.8788 .97963 25 36 395 714 .3435 294 24 36 108 527 .8716 958 24 37 424 745 .3349 288 23 37 136 557 .8644 952 23 38 452 775 .3263 283 22 38 165 588 .8573 946 22 39 481 805 .3178 277 21 39 193 618 .8501 940 21 40 .18509 .18835 5.3093 .98272 20 40 .20222 .20648 4.8430 .97934 20 41 538 865 .3008 267 19 41 250 679 .8359 928 19 42 567 895 .2924 261 18 42 279 709 .8288 922 18 43 595 925 .2839 256 17 43 307 739 .8218 916 17 44 624 955 .2755 250 16 44 336 770 .8147 910 16 45 .18652 .18986 5.2672 .98245 15 45 .20364 .20800 4.8077 .97905 15 46 681 .19016 .2588 240 14 46 393 830 .8007 899 14 47 710 046 .2505 234 13 47 421 861 .7937 893 13 48 738 076 .2422 229 12 48 450 891 .7867 887 12 49 767 106 .2339 223 11 49 478 921 .7798 881 11 50 .18795 .19136 5.2257 .98218 10 50 .20507 .20952 4.7729 .97875 10 51 824 166 .2174 212 9 51 535 .20982 .7659 869 9 52 852 197 .2092 207 8 52 563 .21013 .7591 863 8 53 881 227 .2011 201 7 53 592 043 .7522 857 7 54 910 257 .1929 196 6 54 620 073 .7453 851 6 55 .18938 .19287 5.1848 .98190 5 55 .20649 .21104 4.7385 .97845 5 56 967 317 .1767 185 4 56 677 134 .7317 839 4 57 .18995 347 .1686 179 3 57 706 164 .7249 833 3 58 .19024 378 .1606 174 2 58 734 195 .7181 827 2 59 052 408 .1526 168 1 59 763 225 .7114 821 1 60 .19081 .19438 5.1446 .98163 60 .20791 .21256 4.7046 .97815 c Cos Ctn Tan Sin / Cos Ctn Tan Sin / 79 C 78 C 28 12 Values of Trigonometric Functions 13 C [II 1 Sin Tan Ctn Cos / Sin Tan Ctn Cos .20791 .21256 4.7046 .97815 60 .22495 .23087 4.3315 .97437 60 1 820 286 .6979 809 59 1 523 117 .3257 430 59 2 848 316 .6912 803 58 2 552 148 .3200 424 58 3 877" \ 347 .6845 797 57 3 580 179 .3143 417 57 4 905- 1 377 .6779 791 56 4 608 209 .3086 411 56 5 .20933 .21408 4.6712 .97784 55 5 .22637 .23240 4.3029 .97404 55 6 962 438 .6646 778 54 6 665 271 .2972 398 54 7 .20990 469 .6580 772 53 7 693 301 .2916 391 53 8 .21019 499 .6514 766 52 8 722 332 .2859 384 52 9 047 529 .6448 760 51 9 750 363 .2803 378 51 10 .21076 .21560 4.6382 .97754 50 10 .22778 .23393 4.2747 .97371 50 11 104 590 .6317 748 49 11 807 424 .2691 365 49 12 132 621 .6252 742 48 12 835 455 .2635 358 48 13 161 651 .6187 735 47 13 863 485 .2580 351 47 14 189 682 .6122 729 46 14 892 516 .2524 345 46 15 .21218 .21712 4.6057 .97723 45 15 .22920 .23547 4.2468 .97338 45 16 246 743 .5993 717 44 16 948 578 .2413 331 44 17 275 773 .5928 711 43 17 .22977 608 .2358 325 43 18 303 804 .5864 705 42 18 .23005 639 .2303 318 42 19 331 834 .5800 698 41 19 033 670 .2248 311 41 20 .21360 .21864 4.5736 .97692 40 20 .23062 .23700 4.2193 .97304 40 21 388 895 .5673 686 39 21 090 731 .2139 298 39 22 417 925 .5609 680 38 22 118 762 .2084 291 38 23 445 956 .5546 673 37 23 146 793 .2030 284 37 24 474 .21986 .5483 667 36 24 175 823 .1976 278 36 25 .21502 .22017 4.5420 .97661 35 25 .23203 .23854 4.1922 .97271 35 26 530 047 .5357 655 34 26 231 885 .1868 264 34 27 559 078 .5294 648 33 27 260 916 .1814 257 33 28 587 108 .5232 642 32 28 288 946 .1760 251 32 29 616 139 .5169 636 31 29 316 .23977 .1706 244 31 30 .21644 .22169 4.5107 .97630 30 30 .23345 .24008 4.1653 .97237 30 31 672 200 .5045 623 29 31 373 039 .1600 230 29 32 701 231 .4983 617 28 32 401 069 .1547 223 28 33 729 261 .4922 611 27 33 429 100 .1493 217 27 34 758 292 .4860 604 26 34 458 131 .1441 210 26 35 36 .21786 814 .22322 353 4.4799 .4737 .97598 592 25 24 35 36 723"48'6 J 514 -^4162 193 4.1388 .1335 .97203 196 25 24 37 843 383 .4676 585 23 37 542 223 .1282 189 23 38 871 414 .4615 579 22 38 571 254 .1230 182 22 39 899 444 .4555 573 21 39 599 285 .1178 176 21 40 .21928 .22475 4.4494 .97566 20 40 .23627 .24316 4.1126 .97169 20 41 956 505 .4434 560 19 41 656 347 .1074 162 19 42 .21985 536 .4373 553 18 42 684 377 .1022 155 18 43 .22013 567 .4313 547 17 43 712 408 .0970 148 17 44 041 597 .4253 541 16 44 740 439 .0918 141 16 45 .22070 .22628 4.4194 .97534 15 45 .23769 .24470 4.0867 .9*134 15 46 098 658 .4134 528 14 46 797 501 .0815 127 14 47 126 689 .4075 521 13 47 825 532 .0764 120 13 48 155 719 .4015 515 12 48 853 562 .0713 113 12 49 183 750 .3956 508 11 49 882 593 .0662 106 11 50 .22212 .22781 4.3897 .97502 10 50 .23910 .24624 4.0611 .97100 10 51 240 811 .3838 496 9 51 938 655 .0560 093 9 52 268 842 .3779 489 8 52 966 686 .0509 086 8 53 297 872 .3721 483 7 53 .23995 717 .0459 079 7 54 325 903 .3662 476 6 54 .24023 747 .0408 072 6 55 .22353 .22934 4.3604 .97470 5 55 .24051 .24778 4.0358 .97065 5 56 382 964 .3546 463 4 56 079 809 .0308 058 4 57 410 .22995 .3488 457 3 57 108 840 .0257 051 3 58 438 .23026 .3430 450 2 58 136 871 .0207 044 2 59 467 056 .3372 444 1 59 164 902 .0158 037 1 60 .22495 .23087 4.3315 .97437 60 .24192 .24933 4.0108 .97030 Cos Ctn Tan Sin ' Cos Ctn Tan Sin / IT 76 C II] 14 Values of Trigonometric Functions 15 C 29 1 Sin Tan Ctn Cos / Sin Tan Ctn Cos .24192 .24933 4.0108 .97030 60 .25882 .26795 3.7321 .96593 60 1 220 964 .0058 023 59 1 910 826 .7277 585 59 2 249 .24995 4.0009 015 58 2 938 857 .7234 578 58 3 277 .25026 3.9959 008 57 3 966 888 .7191 570 57 4 305 056 .9910 .97001 56 4 .25994 920 .7148 562 56 5 .24333 .25087 3.9861 .96994 55 5 .26022 .26951 3.7105 .96555 55 6 362 118 .9812 987 54 6 050 .26982 .7062 547 54 7 390 149 .9763 980 53 7 079 .27013 .7019 540 53 8 418 180 .9714 973 52 8 107 044 .6976 532 52 9 446 211 .9665 966 51 9 135 076 .6933 524 51 10 .24474 .25242 3.9617 .96959 50 10 .26163 .27107 3.6891 .96517 50 11 503 273 .9568 952 49 11 191 138 .6848 509 49 12 531 304 .9520 945 48 12 219 169 .6806 502 48 13 559 335 .9471 937 47 13 247 201 .6764 494 47 14 587 366 .9423 930 46 14 275 232 .6722 486 46 15 .24615 .25397 3.9375 .96923 45 15 .26303 .27263 3.6680 .96479 45 16 644 428 .9327 916 44 16 __334- - 294 .6638 471 44 17 672 459 .9279 909 43 17 359 326 .6596 463 43 18 700 490 .9232 902 42 18 387 357 .6554 456 42 19 728 521 .9184 894 41 19 415 388 .6512 448 41 20 .24756 .25552 3.9136 .96887 40 20 .26443 .27419 3.6470 .96440 40 21 784 583 .9089 880 39 21 471 451 .6429 433 39 22 813 614 .9042 873 38 22 500 482 .6387 425 38 23 841 645 .8995 866 37 23 528 513 .6346 417 37 24 869 676 .8947 858 36 24 556 545 .6305 410 36 25 .24897 .25707 3.8900 .96851 35 25 .26584 .27576 3.6264 .96402 35 26 925 738 .8854 844 34 26 612 607 .6222 394 34 27 954 769 .8807 837 33 27 640 638 .6181 386 33 28 :2?9S2 " 800 .8760 829 32 28 668 670 .6140 379 32 29 .25010 831 .8714 822 31 29 696 701 .6100 371 31 30 .25038 .25862 3.8667 .96815 30 30 .26724 .27732 3.6059 .96363 30 31 066 893 .8621 807 29 31 752 764 .6018 355 29 32 094 924 .8575 800 28 32 780 795 .5978 347 28 33 122 955 .8528 793 27 33 808 826 .5937 340 27 34 151 .25986 .8482 786 26 34 836 858 .5897 332 26 35 .25179 .26017 3.8436 .96778 25 35 .26864 .27889 3.5856 .96324 25 36 207 048 .8391 771 24 36 892 921 .5816 316 24 37 235 079 .8345 764 23 37 920 952 .5776 308 23 38 263 110 .8299 756 22 38 948 .27983 .5736 301 22 39 291 141 .8254 749 21 39 .26976 .28015 .5696 293 21 40 .25320 .26172 3.8208 .96742 20 40 .27004 .28046 3.5656 .96285 20 41 348 203 .8163 734 19 41 032 077 .5616 277 19 42 376 235 .8118 727 18 42 060 109 .5576 269 18 43 404 266 .8073 719 17 43 088 140 .5536 261 17 44 432 297 .8028 712 16 44 116 172 .5497 253 16 45 .25460 .26328 3.7983 .96705 15 45 .27144 .28203 3.5457 .96246 15 46 488 359 .7938 697 14 46 172 234 .5418 238 14 47 516 390 .7893 690 13 47 200 266 .5379 230 13 48 545 421 .7848 682 12 48 228 297 .5339 222 12 49 573 452 .7804 675 11 49 256 329 .5300 214 11 50 .25601 .26483 3.7760 .96667 10 50 .27284 .28360 3.5261 .96206 10 51 629 515 .7715 660 9 51 312 391 .5222 198 9 52 657 546 .7671 653 8 52 340 423 .5183 190 8 53 685 577 .7627 645 7 53 368 454 .5144 182 7 54 713 608 .7583 638 6 54 396 486 .5105 174 6 55 .25741 .26639 3.7539 .96630 5 55 .27424 .28517 3.5067 .96166 5 56 769 670 .7495 623 4 56 452 549 .5028 158 4 57 798 701 .7451 615 3 57 480 580 .4989 150 3 58 826 733 .7408 608 2 58 508 612 .4951 142 2 59 854 764 .7364 600 1 59 536 643 .4912 134 1 60 .25882 .26795 3.7321 .96593 60 .27504 .28675 3.4874 .96126 _0_ Cos Ctn Tan Sin / COG Ctn Tan Sin / 75 C 74 C 30 16 Values of Trigonometric Functions 17 C [11 1 Sin Tan Ctn Cos ' Sin Tan Ctn Cos .27564 .28675 3.4874 .96126 60 .29237 .30573 3.2709 .95630 60 1 592 706 .4836 118 59 1 265 605 .2675 622 59 2 620 738 .4798 110 58 2 293 637 .2641 613 58 3 648 769 .4760 102 57 3 321 669 .2607 605 57 4 676/ 801 .4722 094 56 4 348 700 .2573 596 56 5 .27704- .28832 3.4684 .96086 55 5 .29376 .30732 3.2539 .95588 55 6 731 , ,864 .4646 078 54 6 404 764 .2506 579 54 7 759 ' 895 .4608 070 53 7 432 796 .2472 571 53 8 787 927 .4570 062 52 8 460 828 .2438 562 52 9 815 958 .4533 054 51 9 487 860 .2405 554 51 10 .27843 .28990 3.4495 .96046 50 10 .29515 .30891 3.2371 .95545 50 11 871 .29021 .4458 037 49 11 543 923 .2338 536 49 12 899 053 .4420 029 48 12 571 955 .2305 528 48 13 927 084 .4383 021 47 13 599 .30987 .2272 519 47 14 955 116 .4346 013 46 14 626 .31019 .2238 511 46 15 .27983 .29147 3.4308 .96005 45 15 .29654 .31051 3.2205 .95502 45 16 .28011 179 .4271 .95997 44 16 682 083 .2172 493 44 17 039 210 .4234 989 43 17 710 115 .2139 485 43 18 067 242 .4197 981 42 18 737 147 .2106 476 42 19 095 274 .4160 972 41 19 765 178 .2073 467 41 20 .28123 .29305 3.4124 .95964 40 20 .29793 .31210 3.2041 .95459 40 21 150 337 .4087 956 39 21 821 242 .2008 450 39 22 178 368 .4050 948 38 22 849 274 .1975 441 38 23 206 400 .4014 940 37 23 876 306 .1943 433 37 24 234 432 .3977 931 36 24 904 338 .1910 424 36 25 .28262 .29463 3.3941 .95923 35 25 .29932 .31370 3.1878 .95415 35 26 290 495 .3904 915 34 26 960 402 .1845 407 34 27 318 526 .3868 907 33 27 .29987 434 .1813 398 33 28 346 558 .3832 898 32 28 .30015 466 .1780 389 32 29 374 590 .3796 890 31 29 043 498 .1748 380 31 30 .28402 .29621 3.3759 .95882 30 30 .30071 .31530 3.1716 .95372 30 31 429 653 .3723 874 29 31 098 562 .1684 363 29 32 457 685 .3687 865 28 32 126 594 .1652 354 28 33 485 716 .3652 857 27 33 154 626 .1620 345 27 34 513 748 .3616 849 26 34 182 658 .1588 337 26 35 .28541 .29780 3.3580 .95841 25 35 .30209 .31690 3.1556 .95328 25 36 569 811 .3544 832 24 36 237 722 .1524 319 24 37 597 843 .3509 824 23 37 265 754 .1492 310 23 38 625 875 .3473 816 22 38 292 786 .1460 301 22 39 652 906 .3438 807 21 39 320 818 .1429 293 21 40 .28680 .29938 3.3402 .95799 20 40 .30348 .31850 3.1397 .95284 20 41 708 .29970 .3367 791 19 41 376 882 .1366 275 19 42 736 .30001 .3332 782 18 42 403 914 .1334 266 18 43 764 033 .3297 774 17 43 431 946 .1303 257 17 44 792 065 .3261 766 16 44 459 .31978 .1271 248 16 45 .28820 .30097 3.3226 .95757 15 45 .30486 .32010 3.1240 .95240 15 46 847 128 .3191 749 14 46 514 042 .1209 231 14 47 875 160 .3156 740 13 47 542 074 .1178 222 13 48 903 192 .3122 732 12 48 570 106 .1146 213 12 49 931 224 .3087 724 11 49 597 139 .1115 204 11 50 .28959 .30255 3.3052 .95715 10 50 .30625 .32171 3.1084 .95195 10 51 .28987 287 .3017 707 9 51 653 203 .1053 186 9 52 .29015 319 .2983 698 8 52 680 235 .1022 177 8 53 042 351 .2948 690 7 53 708 267 .0991 168 7 54 070 382 .2914 681 6 54 736 299 .0961 159 6 55 .29098 .30414 3.2879 .95673 5 55 .30763 .32331 3.0930 .95150 5 56 126 446 .2845 664 4 56 791 363 .0899 142 4 57 154 478 .2811 656 3 57 819 396 .0868 133 3 58 182 509 .2777 647 2 58 846 428 .0838 124 2 59 209 541 .2743 639 1 59 874 460 .0807 115 1 60 .29237 .30573 3.2709 .95630 60 .30902 .32492 3.0777 .95106 Cos Ctn Tan Sin / Cos Ctn Tan Sin J ' 73 C 72 C II] 18 Values of Trigonometric Functions 19 31 1 Sin Tan Ctn Cos / Sin Tan Ctn Cos .30902 .32492 3.0777 .95106 60 .32557 .34433 2.9042 .94552 60 1 929 524 .0746 097 59 1 584 465 .9015 542 59 2 957 556 .0716 088 58 2 612 498 .8987 533 58 3 .30985 588 .0686 079 57 3 639 530 .8960 523 57 4 .31012 621 .0655 070 56 4 667 563 .8933 514 56 5 .31040 .32653 3.0625 .95061 55 5 .32694 .34596 2.8905 .94504 55 6 068 685 .0595 052 54 6 722 628 .8878 495 54 7 095 717 .0565 043 53 7 749 661 .8851 485 53 8 123 749 .0535 033 52 8 777 693 .8824 476 52 9 151 782 .0505 024 51 9 804 726 .8797 466 51 10 .31178 .32814 3.0475 .95015 50 10 .32832 .34758 2.8770 .94457 50 11 206 846 .0445 .95006 49 11 859 791 .8743 447 49 12 233 878 .0415 .94997 48 12 88^ 824 .8716 438 48 13 261 911 .0385 988 47 13 914 856 .8689 428 47 14 289 943 .0356 979 46 14 942 889 .8662 418 46 15 .31316 .32975 3.0326 .94970 45 15 .32969 .34922 2.8636 .94409 45 16 344 .33007 .0296 961 44 16 .32997 954 .8609 399 44 17 372 040 .0267 952 43 17 .33024 .34987 .8582 390 43 18 399 072 .0237 943 42 18 051 .35020 .8556 380 42 19 427 104 .0208 933 41 19 079 052 .8529 370 41 20 .31454 .33136 3.0178 .94924 40 20 .33106 .35085 2.8502 .94361 40 21 482 169 .0149 915 39 21 134 118 .8476 351 39 22 510 201 .0120 906 38 22 161 150 .8449 342 38 23 537 233 .0090 897 37 23 189 183 .8423 332 37 24 565 266 .0061 888 36 24 216 216 .8397 322 36 25 .31593 .33298 3.0032 .94878 35 25 .33244 .35248 2.8370 .94313 35 26 620 330 3.0003 869 34 26 271 281 .8344 303 34 27 648 363 2.9974 860 33 27 298 314 .8318 293 33 28 675 395 .9945 851 32 28 326 346 .8291 284 32 29 703 427 .9916 842 31 29 353 379 .8265 274 31 30 .31730 .33460 2.9887 .94832 30 30 .33381 .35412 2.8239 .94264 30 31 758 492 .9858 823 29 31 408 445 .8213 254 29 32 786 524 .9829 814 28 32 436 477 .8187 245 28 33 813 557 .9800 805 27 33 463 510 .8161 235 27 34 841 589 .9772 795 26 34 490 543 .8135 225 26 35 .31868 .33621 2.9743 .94786 25 35 .33518 .35576 2.8109 .94215 25 36 896 654 .9714 111 24 36 545 608 .8083 206 24 37 923 686 .9686 768 23 37 573 641 .8057 196 23 38 951 718 .9657 758 22 38 600 674 .8032 186 22 39 .31979 751 .9629 749 21 39 627 707 .8006 176 21 40 .32006 .33783 2.9600 .94740 20 40 .33655 .35740 2.7980 .94167 20 41 034 816 .9572 730 19 41 682 772 .7955 157 19 42 061 848 .9544 721 18 42 710 805 .7929 147 18 43 089 881 .9515 712 17 43 737 838 .7903 137 17 44 116 913 .9487 702 16 44 764 871 .7878 127 16 45 .32144 .33945 2.9459 .94693 15 45 .33792 .35904 2.7852 .94118 15 46 171 .33978 .9431 684 14 46 819 937 .7827 108 14 47 199 .34010 .9403 674 13 47 846 .35969 .7801 098 13 48 227 043 .9375 665 12 48 874 .36002 .7776 088 12 49 254 075 .9347 656 11 49 901 035 .7751 078 11 50 .32282 .34108 2.9319 .94646 10 50 .33929 .36068 2.7725 .94068 10 51 309 140 .9291 637 9 51 956 101 .7700 058 9 52 337 173 .9263 627 8 52 .33983 134 .7675 049 8 53 364 205 .9235 618 7 53 .34011 167 .7650 039 7 54 392 238 .9208 609 6 54 038 199 .7625 029 6 55 .32419 .34270 2.9180 .94599 5 55 .34065 .36232 2.7600 .94019 5 56 447 303 .9152 590 4 56 093 265 .7575 .94009 4 57 474 335 .9125 580 3 57 120 298 .7550 .93999 3 58 502 368 .9097 571 2 58 147 331 .7525 989 2 59 529 400 .9070 561 1 59 175 364 .7500 979 1 60 .32557 .34433 2.9042 .94552 60 .34202 .36397 2.7475 .93969 Cos Ctn Tan Sin ' Cos Ctn Tan Sin / 71 C 70 32 20 Values of Trigonometric Functions 2V [II / Sin Tan Ctn Cos 1 Sin Tan Ctn Cos .34202 .36397 2.7475 .93969 60 .35837 .38386 2.6051 .93358 60 1 229 430 .7450 959 59 1 864 420 .6028 348 59 2 257 463 .7425 949 58 2 891 453 .6006 337 58 3 284 496 .7400 939 57 3 918 487 .5983 327 57 4 311 529 .7376 929 56 4 945 520 .5961 316 56 5 .34339 .36562 2.7351 .93919 55 5 .35973 .38553 2.5938 .93306 55 6 366 595 .7326 909 54 6 .36000 587 .5916 295 54 7 393 628 .7302 899 53 7 027 620 .5893 285 53 8 421 661 .7277 889 52 8 054 654 .5871 274 52 9 448 694 .7253 879 51 9 081 687 .5848 264 51 10 .34475 .36727 2.7228 .93869 50 10 .36108 .38721 2.5826 .93253 50 11 503 760 .7204 859 49 11 135 754 .5804 243 49 12 530 793 .7179 849 48 12 162 787 .5782 232 48 13 557 826 .7155 839 47 13 190 821 .5759 222 47 14 584 859 .7130 829 46 14 217 854 .5737 211 46 15 .34612 .36892 2.7106 .93819 45 15 .36244 .38888 2.5715 .93201 45 16 639 925 .7082 809 44 16 271 921 .5693 190 44 17 666 958 .7058 799 43 17 298 955 .5671 180 43 18 694 .36991 .7034 789 42 18 325 .38988 .5649 169 42 19 721 .37024 .7009 779 41 19 352 .39022 .5627 159 41 20 .34748 .37057 2.6985 .93769 40 20 .36379 .39055 2.5605 .93148 40 21 775 090 .6961 759 39 21 406 089 .5583 137 39 22 803 123 .6937 748 38 22 434 122 .5561 127 38 23 830 157 .6913 738 37 23 461 156 .5539 116 37 24 857 190 .6889 728 36 24 488 190 .5517 106 36 25 .34884 .37223 2.6865 .93718 35 25 .36515 .39223 2.5495 .93095 35 26 912 256 .6841 708 34 26 542 257 .5473 084 34 27 939 289 .6818 698 33 27 569 290 .5452 074 33 28 966 322 .6794 688 32 28 596 324 .5430 063 32 29 .34993 355 .6770 677 31 29 623 357 .5408 052 31 30 .35021 .37388 2.6746 .93667 30 30 .36650 .39391 2.5386 .93042 30 31 048 422 .6723 657 29 31 677 425 .5365 031 29 32 075 455 .6699 647 28 32 704 458 .5343 020 28 33 102 488 .6675 637 27 33 731 492 .5322 .93010 27 34 130 521 .6652 626 26 34 758 526 .5300 .92999 26 35 .35157 .37554 2.6628 .93616 25 35 .36785 .39559 2.5279 .92988 25 36 184 588 .6605 606 24 36 812 593 .5257 978 24 37 211 621 .6581 596 23 37 839 626 .5236 967 23 38 239 654 .6558 585 22 38 867 660 .5214 956 22 39 266 687 .6534 575 21 39 894 694 .5193 945 21 40 .35293 .37720 2.6511 .93565 20 40 .36921 .39727 2.5172 .92935 20 41 320 754 .6488 555 19 41 948 761 .5150 924 19 42 347 787 .6464 544 18 42 .36975 795 .5129 913 18 43 375 820 .6441 534 17 43 .37002 829 .5108 902 17 44 402 853 .6418 524 16 44 029 862 .5086 892 16 45 .35429 .37887 2.6395 .93514 15 45 .37056 .39896 2.5065 .92881 15 46 456 920 .6371 503 14 46 083 930 .5044 870 14 47 484 953 .6348 493 13 47 110 963 .5023 859 13 48 511 .37986 .6325 483 12 48 137 .39997 .5002 849 12 49 538 .38020 .6302 472 11 49 164 .40031 .4981 838 11 50 .35565 .38053 2.6279 .93462 10 50 .37191 .40065 2.4960 .92827 10 51 592 086 .6256 452 9 51 218 098 .4939 816 9 52 619 120 .6233 441 8 52 245 132 .4918 805 8 53 647 153 .6210 431 7 53 272 166 .4897 794 7 54 674 186 .6187 420 6 54 299 200 .4876 784 6 55 .35701 .38220 2.6165 .93410 5 55 .37326 .40234 2.4855 .92773 5 56 728 253 .6142 400 4 56 353 267 .4834 762 4 57 755 286 .6119 389 3 57 380 301 .4813 751 3 58 782 320 .6096 379 2 58 407 335 .4792 740 2 59 810 353 .6074 368 1 59 434 369 .4772 729 1 60 .35837 .38386 2.6051 .93358 c 60 .37461 .40403 2.4751 .92718 Cos Ctn Tan Sin 1 Cos Ctn Tan Sin i 69 C 68 C II] 22 Values of Trigonometric Functions 23 C 33 / Sin Tan Ctn Cos ' Sin Tan Ctn Cos .37461 .40403 2.4751 .92718 60 .39073 .42447 2.3559 .92050 60 1 488 436 .4730 707 59 1 100 482 .3539 039 59 2 515 470 .4709 697 58 2 127 516 .3520 028 58 3 542 504 .4689 686 57 3 153 551 .3501 016 57 4 569 538 .4668 675 56 4 180 585 .3483 .92005 56 5 .37595 .40572 2.4648 .92664 55 5 .39207 .42619 2.3464 .91994 55 6 622 606 .4627 653 54 6 234 654 .3445 982 54 7 649 640 .4606 642 53 7 260 688 .3426 971 53 8 676 674 .4586 631 52 8 287 722 .3407 959 52 9 703 707 .4566 620 51 9 314 757 .3388 948 51 10 .37730 .40741 2.4545 .92609 50 10 .39341 .42791 2.3369 .91936 50 11 757 775 .4525 598 49 11 367 826 .3351 925 49 12 784 809 .4504 587 48 12 394 860 .3332 914 48 13 811 843 .4484 576 47 13 421 894 .3313 902 47 14 838 877 .4464 565 46 14 448 929 .3294 891 46 15 .37865 .40911 2.4443 .92554 45 15 .39474 .42963 2.3276 .91879 45 16 892 945 .4423 543 44 16 501 .42998 .3257 868 44 17 919 .40979 .4403 532 43 17 528 .43032 .3238 856 43 18 946 .41013 .4383 521 42 18 555 067 .3220 845 42 19 973 047 .4362 510 41 19 581 101 .3201 833 41 20 .37999 .41081 2.4342 .92499 40 20 .39608 .43136 2.3183 .91822 40 21 .38026 115 .4322 488 39 21 635 170 .3164 810 39 22 053 149 .4302 477 38 22 661 205 .3146 799 38 23 080 183 .4282 466 37 23 688 239 .3127 787 37 24 107 217 .4262 455 36 24 715 274 .3109 775 36 25 .38134 .41251 2.4242 .92444 35 25 .39741 .43308 2.3090 .91764 35 26 161 285 .4222 432 34 26 768 343 .3072 752 34 27 188 319 .4202 421 33 27 795 378 .3053 741 33 28 215 353 .4182 410 32 28 822 412 .3035 729 32 29 241 387 .4162 399 31 29 848 447 .3017 718 31 30 .38268 .41421 2.4142 .92388 30 30 .39875 .43481 2.2998 .91706 30 31 295 455 .4122 377 29 31 902 V 516 .2980 694 29 32 322 490 .4102 366 28 32 928 550 .2962 683 28 33 349 524 .4083 355 27 33 955 - 585 .2944 671 27 34 376 558 .4063 343 26 34 ~30Q82 620 .2925 660 26 35 .38403 .41592 2.4043 .92332 25 35 .40008 \43654 2.2907 .91648 25 36 430 626 .4023 321 24 36 035 689 .2889 636 24 37 456 660 .4004 310 23 37 062 724 .2871" 625 23 38 483 694 .3984 299 22 38 088 758 .2853 613 22 39 510 728 .3964 287 21 39 115 793 .2835 601 21 40 .38537 .41763 2.3945 .92276 20 40 .40141 .43828 2.2817 .91590 20 41 564 797 .3925 265 19 41 168 862 .2799 578 19 42 591 831 .3906 254 18 42 195 897 .2781 566 18 43 617 865 .3886 243 17 43 221 932 .2763 555 17 44 644 899 .3867 231 16 44 248 .43966 .2745 543 16 45 .38671 .41933 2.3847 .92220 15 45 .40275 .44001 2.2727 .91531 15 46 698 .41968 .3828 209 14 46 301 036 .2709 519- 14 47 725 .42002 .3808 198 13 47 328 071 .2691 508 13 48 752 036 .3789 186 12 48 355 105 .2673 496 12 49 778 070 .3770 175 11 49 381 140 .2655 484 11 50 .38805 .42105 2.3750 .92164 10 50 .40408 .44175 2.2637 .91472 10 51 832 139 .3731 152 9 51 434 210 .2620 461 9 52 859 173 .3712 141 8 52 461 244 .2602 449 8 53 886 207 .3693 130 7 53 488 279 .2584 437 7 54 912 242 .3673 119 6 54 514 314 .2566 425 6 55 .38939 .42276 2.3654 .92107 5 55 .40541 .44349 2.2549 .91414 5 56 966 310 .3635 096 4 56 567 384 .2531 402 4 57 .38993 345 .3616 085 3 57 594 418 .2513 390 3 58 .39020 379 .3597 073 2 58 621 453 .2496 378 2 59 046 413 .3578 062 1 59 647 488 .2478 366 1 60 .39073 .42447 2.3559 .92050 60 .40674 .44523 2.2460 .91355 Cos Ctn Tan Sin / Cos Ctn Tan Sin i 67 C 66 C 34 24 Values of Trigonometric Functions 25 C / Sin Tan Ctn Cos / Sin Tan Ctn Cos .40674 .44523 2.2460 .91355 60 .42262 .46631 2.1445 .90631 60 1 700 558 .2443 343 59 1 288 666 .1429 618 59 2 727 593 .2425 331 58 2 315 702 .1413 606 58 3 753 627 .2408 319 57 3 341 737 .1396 594 57 4 780 662 .2390 307 56 4 367 772 .1380 582 56 5 .40806 .44697 2.2373 .91295 55 5 .42394 .46808 2.1364 .90569 55 6 833 732 .2355 283 54 6 420 843 .1348 557 54 7 860 767 .2338 272 53 7 446 879 .1332 545 53 8 886 802 .2320 260 52 8 473 914 .1315 532 52 9 913 837 .2303 248 51 9 499 950 .1299 520 51 10 .40939 .44872 2.2286 .91236 50 10 .42525 .46985 2.1283 .90507 50 11 966 907 .2268 224 49 11 552 .47021 .1267 495 49 12 .40992 942 .2251 212 48 12 578 056 .1251 483 48 13 .41019 .44977 .2234 200 47 13 604 092 .1235 470 47 14 045 .45012 .2216 188 46 14 631 128 .1219 458 46 15 .41072 .45047 2.2199 .91176 45 15 .42657 .47163 2.1203 .90446 45 16 098 082 .2182 164 44 16 683 199 .1187 433 44 17 125 117 .2165 152 43 17 709 234 .1171 421 43 18 151 152 .2148 140 42 18 736 270 .1155 408 42 19 178 187 .2130 128 41 19 762 305 .1139 396 41 20 .41204 .45222 2.2113 .91116 40 20 .42788 .47341 2.1123 .90383 40 21 231 257 .2096 104 39 21 815 377 .1107 371 39 22 257 292 .2079 092 38 22 841 412 .1092 358 38 23 284 327 .2062 080 37 23 867 448 .1076 346 37 24 310 362 .2045 068 36 24 894 483 .1060 334 36 25 .41337 .45397 2.2028 .91056 35 25 .42920 .47519 2.1044 .90321 35 2G 363 432 .2011 044 34 26 946 555 .1028 309 34 27 390 467 .1994 032 33 27 972 590 .1013 296 33 28 416 502 .1977 020 32 28 .42999 626 .0997 284 32 29 443 538 .1960 .91008 31 29 .43025 662 .0981 271 31 30 .41469 .45573 2.1943 .90996 30 30 .43051 .47698 2.0965 .90259 30 31 496 608 .1926 984 29 31 077 733 .0950 246 29 32 522 643 .1909 972 28 32 104 769 .0934 233 28 33 549 678 .1892 960 27 33 130 805 .0918 221 27 34 575 713 .1876 948 26 34 156 840 .0903 208 26 35 .41602 .45748 2.1859 .90936 25 35 .43182 .47876 2.0887 .90196 25 36 628 784 .1842 924 24 36 209 912 .0872 183 24 37 655 819 .1825 911 23 37 235 948 .0856 171 23 38 681 854 .1808 899 22 38 261 .47984 .0840 158 22 39 707 889 .1792 887 21 39 287 .48019 .0825 146 21 40 .41734 .45924 2.1775 .90875 20 40 .43313 .48055 2.0809 .90133 20 41 760 960 .1758 863 19 41 340 091 .0794 120 19 42 787 .45995 .1742 851 18 42 366 127 .0778 108 18 43 813 .46030 .1725 839 17 43 392 163 .0763 095 17 44 840 065 .1708 826 16 44 418 198 .0748 082 16 45 .41866 .46101 2.1692 .90814 15 45 .43445 .48234 2.0732 .90070 15 46 892 136 .1675 802 14 46 471 270 .0717 057 14 47 919 171 .1659 790 13 47 497 306 .0701 045 13 48 945 206 .1642 778 12 48 523 342 .0686 032 12 49 972 242 .1625 766 11 49 549 378 .0671 019 11 50 .41998 .46277 2.1609 .90753 10 50 .43575 .48414 2.0655 .90007 10 51 .42024 312 .1592 741 9 51 602 450 .0640 .89994 9 52 051 348 .1576 729 8 52 628 486 .0625 981 8 53 077 383 .1560 717 7 53 654 521 .0609 968 7 54 104 418 .1543 704 6 54 680 557 .0594 956 6 55 .42130 .46454 2.1527 .90692 5 55 .43706 .48593 2.0579 .89943 5 56 156 489 .1510 680 4 56 733 629 .0564 930 4 57 183 525 .1494 668 3 57 759 665 .0549 918 3 58 209 560 .1478 655 2 58 785 701 .0533 905 2 59 235 595 .1461 643 1 59 811 737 .0518 892 1 60 .42262 .46631 2.1445 .90631 60 .43837 .48773 2.0503 .89879 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 65 C II] 26 Values of Trigonometric Functions 35 t Sin Tan Ctn Cos ' Sin Tan Ctn Cos .43837 .48773 2.0503 .89879 60 .45399 .50953 1.9626 .89101 60 1 863 809 .0488 867 59 1 425 .50989 .9612 087 59 2 889 845 .0473 854 58 2 451 .51026 .9598 074 58 3 916 881 .0458 841 57 3 477 063 .9584 061 57 4 942 917 .0443 828 56 4 503 099 .9570 048 56 5 .43968 .48953 2.0428 .89816 55 5 .45529 .51136 1.9556 .89035 55 6 .43994 .48989 .0413 803 54 6 554 173 .9542 021 54 7 .44020 .49026 .0398 790 53 7 580 209 .9528 .89008 53 8 046 062 .0383 777 52 8 606 246 .9514 .88995 52 9 072 098 .0368 764 51 9 632 283 .9500 981 51 10 .44098 .49134 2.0353 .89752 50 10 .45658 .51319 1.9486 .88968 50 11 124 170 .0338 739 49 11 684 356 .9472 955 49 12 151 206 .0323 726 48 12 710 393 .9458 942 48 13 177 242 .0308 713 47 13 736 430 .9444 928 47 14 203 278 .0293 700 46 14 762 467 .9430 915 46 15 .44229 .49315 2.0278 .89687 45 15 .45787 .51503 1.9416 .88902 45 16 255 351 .0263 674 44 16 813 540 .9402 888 44 17 281 387 .0248 662 43 17 839 577 .9388 875 43 18 307 423 .0233 649 42 18 865 614 .9375 862 42 19 333 459 .0219 636 41 19 891 651 .9361 848 41 20 .44359 .49495 2.0204 .89623 40 20 .45917 .51688 1.9347 .88835 40 21 385 532 .0189 610 39 21 942 724 .9333 822 39 22 411 568 .0174 597 38 22 968 761 .9319 808 38 23 437 604 .0160 584 37 23 .45994 798 .9306 795 37 24 464 640 .0145 571 36 24 .46020 835 .9292 782 36 25 .44490 .49677 2.0130 .89558 35 25 .46046 .51872 1.9278 .88768 35 26 516 713 .0115 545 34 26 072 909 .9265 755 34 27 542 749 .0101 532 33 27 097 946 .9251 741 33 28 568 786 .0086 519 32 28 123 .51983 .9237 728 32 29 594 822 .0072 506 31 29 149 .52020 .9223 715 31 30 .44620 .49858 2.0057 .89493 30 30 .46175 .52057 1.9210 .88701 30 31 646 894 .0042 480 29 31 201 094 .9196 688 29 32 672 931 .0028 467 28 32 226 131 .9183 674 28 33 698 .49967 2.0013 454 27 33 252 168 .9169 661 27 34 724 .50004 ^9999 441 26 34 278 205 .9155 647 26 35 .44750 .50040 1.9984 .89428 25 35 .46304 .52242 1.9142 .88634 25 36 776 076 .9970 415 24 36 330 279 .9128 620 24 37 802 113 .9955 402 23 37 355 316 .9115 607 23 38 828 149 .9941 389 22 38 381 353 .9101 593 22 39 854 185 .9926 376 21 39 407 390 .9088 580 21 40 .44880 .50222 1.9912 .89363 20 40 .46433 .52427 1.9074 .88566 20 41 906 258 .9897 350 19 41 458 464 .9061 553 19 42 932 295 .9883 337 18 42 484 501 .9047 539 18 43 958 331 .9868 324 17 43 510 538 .9034 526 17 44 .44984 368 .9854 311 16 44 536 575 .9020 512 16 45 .45010 .50404 1.9840 .89298 15 45 .46561 .52613 1.9007 .88499 15 46 036 441 .9825 285 14 46 587 650 .8993 485 14 47 062 477 .9811 272 13 47 613 687 .8980 472 13 48 088 514 .9797 259 12 48 639 724 .8967 458 12 49 114 550 .9782 245 11 49 664 761 .8953 445 11 50 .45140 .50587 1.9768 .89232 10 50 .46690 .52798 1.8940 .88431 10 51 166 623 .9754 219 9 51 716 836 .8927 417 9 52 192 660 .9740 206 8 52 742 873 .8913 404 8 53 218 696 .9725 193 7 53 767 910 .8900 390 7 54 243 733 .9711 180 6 54 793 947 .8887 377 6 55 .45269 .50769 1.9697 .89167 5 55 .46819 .52985 1.8873 .88363 5 56 295 806 .9683 153 4 56 844 .53022 .8860 349 4 57 321 843 .9669 140 3 57 870 059 .8847 336 3 58 347 879 .9654 127 2 58 .896 096 .8834 322 2 59 373 916 .9640 114 1 59 921 134 .8820 308 1 60 .45399 .50953 1.9626 .89101 60 .46947 .53171 1.8807 .88295 Cos Ctn Tan Sin / Cos Ctn Tan Sin 1 63 C 62 C 36 28 Values of Trigonometric Functions 29 e / Sin Tan Ctn Cos i Sin Tan Ctn Cos .46947 .53171 1.8807 .88295 60 .48481 .55431 1.8040 .87462 60 1 973 208 .8794 281 59 1 506 469 .8028 448 59 2 .46999 246 .8781 267 58 2 532 507 .8016 434 58 3 .47024 283 .8768 254 57 3 557 545 .8003 420 57 4 050 320 .8755 240 56 4 583 583 .7991 406 56 5 .47076 .53358 1.8741 .88226 55 5 .48608 .55621 1.7979 .87391 55 6 101 395 .8728 213 54 6 634 659 .7966 377 54 7 127 432 .8715 199 53 7 659 697 .7954 363 53 8 153 470 .8702 185 52 8 684 736 .7942 349 52 9 178 507 .8689 172 51 9 710 774 .7930 335 51 10 .47204 .53545 1.8676 .88158 50 10 .48735 .55812 1.7917 .87321 50 11 229 582 .8663 144 49 11 761 850 .7905 306 49 12 255 620 .8650 130 48 12 786 888 .7893 292 48 13 281 657 .8637 117 47 13 811 926 .7881 278 47 14 306 694 .8624 103 46 14 837 .55964 .7868 264 46 15 .47332 .53732 1.8611 .88089 45 15 .48862 .56003 1.7856 .87250 45 16 358 769 .8598 075 44 16 888 041 .7844 235 44 17 383 807 .8585 062 43 17 913 079 .7832 221 43 18 409 844 .8572 048 42 18 938 117 .7820 207 42 19 434 882 .8559 034 41 19 964 156 .7808 193 41 20 .47460 .53920 1.8546 .88020 40 20 .48989 .56194 1.7796 .87178 40 21 486 957 .8533 .88006 39 21 .49014 232 .7783 164 39 22 511 .53995 .8520 .87993 38 22 040 270 .7771 150 38 23 537 .54032 .8507 979 37 23 065 309 .7759 136 37 24 562 070 .8495 965 36 24 090 347 .7747 121 36 25 .47588 .54107 1.8482 .87951 35 25 .49116 .56385 1.7735 .87107 35 26 614 145 .8469 937 34 26 141 424 .7723 093 34 27 639 183 .8456 923 33 27 166 462 .7711 079 33 28 665 220 .8443 909 32 28 192 501 .7699 064 32 29 690 258 .8430 896 31 29 217 539 .7687 050 31 30 .47716 .54296 1.8418 .87882 30 30 .49242 .56577 1.7675 .87036 30 31 741 333 .8405 868 29 31 268 616 .7663 021 29 32 767 371 .8392 854 28 32 293 654 .7651 .87007 28 33 793 409 .8379 840 27 33 318 693 .7639 .86993 27 34 818 446 .8367 826 26 34 344 731 .7627 978 26 35 .47844 .54484 1.8354 .87812 25 35 .49369 .56769 1.7615 .86964 25 36 869 522 .8341 798 24 36 394 808 .7603 949 24 37 895 560 .8329 784 23 37 419 846 .7591 935 23 38 920 597 .8316 770 22 38 445 885 .7579 921 22 39 946 635 .8303 756 21 39 470 923 .7567 906 21 40 .47971 .54673 1.8291 .87743 20 40 .49495 .56962 1.7556 .86892 20 41 .47997 711 .8278 729 19 41 521 .57000 .7544 878 19 42 .48022 748 .8265 715 18 42 546 039 .7532 863 18 43 048 786 .8253 701 17 43 571 078 .7520 849 17 44 073 824 .8240 687 16 44 596 116 .7508 834 16 45 .48099 .54862 1.8228 .87673 15 45 .49622 .57155 1.7496 .86820 15 46 124 900 .8215 659 14 46 647 193 .7485 805 14 47 150 938 .8202 645 13 47 672 232 .7473 791 13 48 175 .54975 .8190 631 12 48 697 271 .7461 111 12 49 201 .55013 .8177 617 11 49 723 309 .7449 762 11 50 .48226 .55051 1.8165 .87603 10 50 .49748 .57348 1.7437 .86748 10 51 252 089 .8152 589 9 51 773 386 .7426 733 9 52 277 127 .8140 575 8 52 798 425 .7414 719 8 53 303 165 .8127 561 7 53 824 464 .7402 704 7 54 328 203 .8115 546 6 54 849 503 .7391 690 6 55 .48354 .55241 1.8103 .87532 5 55 .49874 .57541 1.7379 .86675 5 56 379 279 .8090 518 4 56 899 580 .7367 661 4 57 405 317 .8078 504 3 57 924 619 .7355 646 3 58 430 355 .8065 490 2 58 950 657 .7344 632 2 59 456 393 .8053 476 1 59 .49975 696 .7332 617 1 60 .48481 .55431 1.8040 .87462 60 .50000 .57735 1.7321 .86603 _0 Cos Ctn Tan Sin i Cos Ctn Tan Sin i 61 C 60 C II] 30 Values of Trigonometric Functions 31 C 37 ' Sin Tan Ctn Cos / Sin Tan Ctn Cos .50000 .57735 1.7321 .86603 60 .51504 .60086 1.6643 .85717 60 1 025 774 .7309 588 59 1 529 126 .6632 702 59 2 050 813 .7297 573 58 2 554 165 .6621 687 58 3 076 851 .7286 559 57 3 579 205 .6610 672 57 4 101 890 .7274 544 56 4 604 245 .6599 657 56 5 .50126 .57929 1.7262 .86530 55 5 .51628 .60284 1.6588 .85642 55 6 151 .57968 .7251 515 54 6 653 324 .6577 627 54 7 176 .58007 .7239 501 53 7 678 364 .6566 612 53 8 201 046 .7228 486 52 8 703 403 .6555 597 52 9 227 085 .7216 471 51 9 728 443 .6545 582 51 10 .50252 .58124 1.7205 .86457 50 10 .51753 .60483 1.6534 .85567 50 11 277 162 .7193 442 49 11 778 522 .6523 551 49 12 302 201 .7182 427 48 12 803 562 .6512 536 48 13 327 240 .7170 413 47 13 828 602 .6501 521 47 14 352 279 .7159 398 46 14 852 642 .6490 506 46 15 .50377 .58318 1.7147 .86384 45 15 .51877 .60681 1.6479 .85491 45 16 403 357 .7136 369 44 16 902 721 .6469 476 44 17 428 396 .7124 354 43 17 927 761 .6458 461 43 18 453 435 .7113 340 42 18 952 801 .6447 446 42 19 478 474 .T102 325 41 19 .51977 841 .6436 431 41 20 .50503 .58513 1.7090 .86310 40 20 .52002 .60881 1.6426 .85416 40 21 528 552 .7079 295 39 21 026 921 .6415 401 39 22 553 591 .7067 281 38 22 051 .60960 .6404 385 38 23 578 631 .7056 266 37 23 076 .61000 .6393 370 37 24 603 670 .7045 251 36 24 101 040 .6383 355 36 25 .50628 .58709 1.7033 .86237 35 25 .52126 .61080 1.6372 .85340 35 26 654 748 .7022 222 34 26 151 120 .6361 325 34 27 679 787 .7011 207 33 27 175 160 .6351 310 33 28 704 826 .6999 192 32 28 200 200 .6340 294 32 29 729 865 .6988 178 31 29 225 240 .6329 279 31 30 .50754 .58905 1.6977 .86163 30 30 .52250 .61280 1.6319 .85264 30 31 779 944 .6965 148 29 31 275 320 .6308 249 29 32 804 .58983 .6954 133 28 32 299 360 .6297 234 28 33 829 .59022 .6943 119 27 33 324 400 .6287 218 27 34 854 061 .6932 104 26 34 349 440 .6276 203 26 35 .50879 .59101 1.6920 .86089 25 35 .52374 .61480 1.6265 .85188 25 36 904 140 .6909 074 24 36 399 520 .6255 173 24 37 929 179 .6898 059 23 37 423 561 .6244 157 23 38 954 218 .6887 045 22 38 448 601 .6234 142 22 39 .50979 258 .6875 030 21 39 473 641 .6223 127 21 40 .51004 .59297 1.6864 .86015 20 40 .52498 .61681 1.6212 .85112 20 41 029 336 .6853 .86000 19 41 522 721 .6202 096 19 42 054 376 .6842 .85985 18 42 547 761 .6191 081 18 43 079 415 .6831 970 17 43 572 801 .6181 066 17 44 104" 454 .6820 956 16 44 597 842 .6170 051 16 45 .51129 .59494 1.6808 .85941 15 45 .52621 .61882 1.6160 .85035 15 46 154 533 .6797 926 14 46 646 922 .6149 020 14 47 179 573 .6786 911 13 47 671 .61962 .6139 .85005 13 48 204 612 .6775 896 12 48 696 .62003 .6128 .84989 12 49 229 651 .6764 881 11 49 720 043 .6118 974 11 50 .51254 .59691 1.6753 .85866 10 50 .52745 .62083 1.6107 .84959 10 51 279 730 .6742 851 9 51 770 124 .6097 943 9 52 304 770 .6731 836 8 52 794 164 .6087 928 8 53 320 809 .6720 821 7 53 819 204 .6076 913 7 54 354 849 .6709 806 6 54 844 245 .6066 897 6 55 .51379 .59888 1.6698 .85792 5 55 .52869 .62285 1.6055 .84882 5 56 404 928 .6687 111 4 56 893 325 .6045 866 4 57 429 .59967 .6676 762 3 57 918 366 .6034 851 3 58 454 .60007 .6665 747 2 58 943 406 .6024 836 2 59 479 046 .6654 732 1 59 967 446 .6014 820 1 60 .51504 .60086 1.6643 .85717 60 .52992 .62487 1.6003 .84805 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 59 58 C 38 32 Values of Trigonometric Functions 33 C / Sin Tan Ctn Cos / Sin Tan Ctn Cos .52992 .62487 1.6003 .84805 60 .54464 .64941 1.5399 .83867 60 1 .53017 527 .5993 789 59 1 488 .64982 .5389 851 59 2 041 568 .5983 774 58 2 513 .65024 .5379 835 58 3 066 608 .5972 759 57 3 537 065 .5369 819 57 4 091 649 .5962 743 56 4 561 106 .5359 804 56 5 .53115 .62689 1.5952 .84728 55 5 .54586 .65148 1.5350 .83788 55 6 140 730 .5941 712 54 6 610 189 .5340 111 54 7 164 770 .5931 697 53 7 635 231 .5330 756 53 8 189 811 .5921 681 52 8 659 272 .5320 740 52 9 214 852 .5911 666 51 9 683 314 .5311 724 51 10 .53238 .62892 1.5900 .84650 50 10 .54708 .65355 1.5301 .83708 50 11 263 933 .5890 635 49 11 732 397 .5291 692 49 12 288 .62973 .5880 619 48 12 756 438 .5282 676 48 13 312 .63014 .5869 604 47 13 781 480 .5272 660 47 14 337 055 .5859 588 46 14 805 521 .5262 645 46 15 .53361 .63095 1.5849 .84573 45 15 .54829 .65563 1.5253 .83629 45 16 386 136 .5839 557 44 16 854 604 .5243 613 44 17 411 177 .5829 542 43 17 878 646 .5233 597 43 18 435 217 .5818 526 42 18 902 688 .5224 581 42 19 460 258 .5808 511 41 19 927 729 .5214 565 41 20 .53484 .63299 1.5798 .84495 40 20 .54951 .65771 1.5204 .83549 40 21 509 340 .5788 480 39 21 975 813 .5195 533 39 22 534 380 .5778 464 38 22 .54999 854 .5185 517 38 23 558 421 .5768 448 37 23 .55024 896 .5175 501 37 24 583 462 .5757 433 36 24 048 938 .5166 485 36 25 .53607 .63503 1.5747 .84417 35 25 .55072 .65980 1.5156 .83469 35 26 632 544 .5737 402 34 26 097 .66021 .5147 453 34 27 656 584 .5727 386 33 27 121 063 .5137 437 33 28 681 625 .5717 370 32 28 145 105 .5127 421 32 29 705 666 .5707 355 31 29 169 147 .5118 405 31 30 .53730 .63707 1.5697 .84339 30 30 .55194 .66189 1.5108 .83389 30 31 754 748 .5687 324 29 31 218 230 .5099 373 29 32 779 789 .5677 308. 28 32 242 272 .5089 356 28 33 804 830 .5667 292 27 33 266 314 .5080 340 27 34 828 871 .5657 277 26 34 291 356 .5070 324 26 35 .53853 .63912 1.5647 .84261 25 35 .55315 .66398 1.5061 .83308 25 30 877 953 .5637 245 24 36 339 440 .5051 292 24 37 902 .63994 .5627 230 23 37 363 482 .5042 276 23 38 926 .64035 .5617 214 22 38 388 524 .5032 260 22 39 951 076 .5607 198 21 39 412 566 .5023 244 21 40 .53975 .64117 1.5597 .84182 20 40 .55436 .66608 1.5013 .83228 20 41 .54000 158 .5587 167 19 41 460 650 .5004 212 19 42 024 199 .5577 151 18 42 484 692 .4994 195 18 43 049 240 .5567 135 17 43 509 734 .4985 179 17 44 073 281 .5557 120 16 44 533 776 .4975 163 16 45 .54097 .64322 1.5547 .84104 15 45 .55557 .66818 1.4966 .83147 15 46 122 363 .5537 088 14 46 581 860 .4957 131 14 47 146 404 .5527 072 13 47 605 902 .4947 115 13 48 171 446 .5517 057 12 48 630 944 .4938 098 12 49 195 487 .5507 041 11 49 65~4 .66986 .4928 082 11 50 .54220 .64528 1.5497 .84025 10 50 .55678 .67028 1.4919 .83066 10 51 244 569 .5487 .84009 9 51 702 071 .4910 050 9 52 269 610 .5477 .83994 8 52 726 113 .4900 034 8 53 293 652 .5468 978 7 53 750 155 .4891 017 7 54 317 693 .5458 962 & 54 775 197 .4882 .83001 6 55 .54342 .64734 1.5448 .83946 5 55 .55799 .67239 1.4872 .82985 5 56 366 775 .5438 930 4 56 823 282 .4863 969 4 57 391 817 .5428 915 3 57 847 324 .4854 953 3 58 415 858 .5418 899 2 58 871 366 .4844 936 2 59 440 899 .5408 883 1 59 895 409 .4835 920 1 60 .54464 .64941 1.5399 .83867 60 .55919 .67451 1.4826 .82904 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 57 C 56 C II] 34 Values of Trigonometric Functions 35 e / Sin Tan Ctn Cos / Sin Tan Ctn Cos 55919 .67451 1.4826 .82904 60 .57358 .70021 1.4281 .81915 60 1 943 493 .4816 887 59 1 381 064 .4273 899 59 2 968 536 .4807 871 58 2 405 107 .4264 882 58 3 55992 578 .4798 855 57 3 429 151 .4255 865 57 4 56016 620 .4788 839 56 4 453 194 .4246 848 56 5 56040 .67663 1.4779 .82822 55 5 .57477 .70238 1.4237 .81832 55 6 064 705 .4770 806 54 6 501 281 .4229 815 54 7 088 748 .4761 790 53 7 524 325 .4220 798 53 8 112 790 .4751 773 52 8 548 368 .4211 782 52 9 136 832 .4742 757 51 9 572 412 .4202 765 51 10 56160 .67875 1.4733 .82741 50 10 .57596 .70455 1.4193 .81748 50 11 184 917 .4724 724 49 11 619 499 .4185 731 49 12 208 .67960 .4715 708 48 12 643 542 .4176 714 48 13 232 .68002 .4705 692 47 13 667 586 .4167 698 47 14 256 045 .4696 675 46 14 691 629 .4158 681 46 15 .56280 .68088 1.4687 .82659 45 15 .57715 .70673 1.4150 .81664 45 16 305 130 .4678 643 44 16 738 717 .4141 647 44 17 329 173 .4669 626 43 17 762 760 .4132 631 43 18 353 215 .4659 610 42 18 786 804 .4124 614 42 19 377 258 .4650 593 41 19 810 848 .4115 597 41 20 .56401 .68301 1.4641 .82577 40 20 .57833 .70891 1.4106 .81580 40 21 425 343 .4632 561 39 21 857 935 .4097 563 39 22 449 386 .4623 544 38 22 881 .70979 .4089 546 38 23 473 429 .4614 528 37 23 904 .71023 .4080 530 37 24 497 471 .4605 511 36 24 928 066 .4071 513 36 25 .56521 .68514 1.4596 .82495 35 25 .57952 .71110 1.4063 .81496 35 26 545 557 .4586 478 34 26 976 154 .4054 479 34 27 569 600 .4577 462 33 27 .57999 198 .4045 462 33 28 593 642 .4568 446 32 28 .58023 242 .4037 445 32 29 617 685 .4559 429 31 29 047 285 .4028 428 31 30 .56641 .68728 1.4550 .82413 30 30 .58070 .71329 1.4019 .81412 30 31 665 771 .4541 396 29 31 094 373 .4011 395 29 32 689 814 .4532 380 28 32 118 417 .4002 378 28 33 713 857 .4523 363 27 33 141 461 .3994 361 27 34 736 900 .4514 347 26 34 165 505 .3985 344 26 35 .56760 .68942 1.4505 .82330 25 35 .58189 .71549 1.3976 .81327 25 36 784 .68985 .4496 314 24 36 212 593 .3968 310 24 37 808 .69028 .4487 297 23 37 236 637 .3959 293 23 38 832 071 .4478 281 22 38 260 681 .3951 276 22 39 856 114 .4469 264 21 39 283 725 .3942 259 21 40 .56880 .69157 1.4460 .82248 20 40 .58307 .71769 1.3934 .81242 20 41 904 200 .4451 231 19 41 330 813 .3925 225 19 42 928 243 .4442 214 18 42 354 857 .3916 208 18 43 952 286 .4433 198 17 43 378 901 .3908 191 17 44 .56976 329 .4424 181 16 44 401 946 .3899 174 16 45 .57000 .69372 1.4415 .82165 15 45 .58425 .71990 1.3891 .81157 15 46 024 416 .4406 148 14 46 449 .72034 .3882 140 14 47 047 459 .4397 132 13 47 472 078 .3874 123 13 48 071 502 .4388 115 12 48 496 122 .3865 106 12 49 095 545 .4379 098 11 49 519 167 .3857 089 11 50 .57119 .69588 1.4370 .82082 10 50 .58543 .72211 1.3848 .81072 10 51 143 631 .4361 065 9 51 567 255 .3840 055 9 52 167 675 .4352 048 8 52 590 299 .3831 038 8 53 191 718 .4344 032 7 53 614 344 .3823 021 7 54 215 761 .4335 .82015 6 54 637 388 .3814 .81004 6 55 .57238 .69804 1.4326 .81999 5 55 .58661 .72432 1.3806 .80987 5 56 262 847 .4317 982 4 56 684 477 .3798 970 4 57 286 891 .4308 965 3 57 708 521 .3789 953 3 58 310 934 .4299 949 2 58 731 565 .3781 936 2 59 334 .69977 .4290 932 1 59 755 610 .3772 919 1 60 .57358 .70021 1.4281 .81915 60 .58779 .72654 1.3764 .80902 Cos Ctn Tan Sin / Cos Ctn Tan Sin ' 55 C 54 C 40 36 Values of Trigonometric Functions 37 C [II / Sin Tan Ctn Cos / Sin Tan Ctn Cos .58779 .72654 1.3764 .80902 60 .60182 .75355 1.3270 .79864 60 1 802 699 .3755 885 59 1 205 401 .3262 846 59 2 826 743 .3747 867 58 2 228 447 .3254 829 58 3 849 788 .3739 850 57 3 251 492 .3246 811 57 4 873 832 .3730 833 56 4 274 538 .3238 793 56 5 .58896 .72877 1.3722 .80816 55 5 .60298 .75584 1.32.30 .79776 55 6 920 921 .3713 799 54 6 321 629 .3222 758 54 7 943 .72966 .3705 782 53 7 344 675 .3214 741 53 8 967 .73010 .3697 765 52 8 367 721 .3206 723 52 9 .58990 055 .3688 748 51 9 390 767 .3198 706 51 10 .59014 .73100 1.3680 .80730 50 10 .60414 .75812 1.3190 .79688 50 11 037 144 .3672 713 49 11 437 858 .3182 671 49 12 061 189 .3663 696 48 12 460 904 .3175 653 48 13 084 234 .3655 679 47 13 483 950 .3167 635 47 14 108 278 .3647 662 46 14 506 .75996 .3159 618 46 15 .59131 .73323 1.3638 .80644 45 15 .60529 .76042 1.3151 .79600 45 16 154 368 .3630 627 44 16 553 088 .3143 583 44 17 178 413 .3622 610 43 17 576 134 .3135 565 43 18 201 457 .3613 593 42 18 599 180 .3127 547 42 19 225 502 .3605 "576 41 19 622 226 .3119 530 41 20 .59248 .73547 1.3597 .80558 40 20 .60645 .76272 1.3111 .79512 40 21 272 592 .3588 541 39 21 668 318 .3103 494 39 22 295 637 .3580 524 38 22 691 364 .3095 477 38 23 318 681 .3572 507 37 23 714 410 .3087 459 37 24 342 726 .3564 489 36 24 738 456 .3079 441 36 25 .59365 .73771 1.3555 .80472 35 25 .60761 .76502 1.3072 .79424 35 26 389 816 .3547 455 34 26 784 548 .3064 406 34 27 412 861 .3539 438 33 27 807 594 .3056 388 33 28 436 906 .3531 420 32 28 830 640 .3048 371 32 29 459 951 .3522 403 31 29 853 686 .3040 353 31 30 .59482 .73996 1.3514 .80386 30 30 .60876 .76733 1.3032 .79335 30 31 506 .74041 .3506 368 29 31 899 779 .3024 318 29 32 529 086 .3498 351 28 32 922 825 .3017 300 28 33 552 131 .3490 334 27 33 945 871 .3009 282 27 34 576 176 .3481 316 26 34 968 918 .3001 264 26 35 .59599 .74221 1.3473 .80299 25 35 .60991 .76964 1.2993 .79247 25 36 622 267 .3465 282 24 36 .61015 .77010 .2985 229 24 37 646 312 .3457 264 23 37 038 057 .2977 211 23 38 669 357 .3449 247 22 38 061 103 .2970 193 22 39 693 402 .3440 230 21 39 084 149 .2962 176 2J 40 .59716 .74447 1.3432 .80212 20 40 .61107 .77196 1.2954 .79158 20 41 739 492 .3424 195 19 41 130 242 .2946 140 19 42 763 538 .3416 178 18 42 153 289 .2938 122 18 43 786 583 .3408 160 17 43 176 335 .2931 105 17 44 809 628 .3400 143 16 44 199 382 .2923 087 16 45 .59832 .74674 1.3392 .80125 15 45 .61222 .77428 1.2915 .79069 15 46 856 719 .3384 108 14 46 245 475 .2907 051 14 47 879 764 .3375 091 13 47 268 521 .2900 033 13 48 902 810 .3367 073 12 48 291 568 .2892 .79016 12 49 926 855 .3359 056 11 49 314 615 .2884 .78998 11 50 .59949 .74900 1.3351 .80038 10 50 .61337 .77661 1.2876 .78980 10 51 972 946 .3343 021 9 51 360 708 .2869 962 9 52 ,59996 .74991 .3335 .800(13 & 52 383 754 .2861 944 8 53 .60019 .75037 .3327 7799801 7 53 406 801 .2853 926 7 54 042 082 .3319 968 G 54 429 848 .2846 908 6 55 .60065 .75128 1.3311 .79951 5 55 .61451 .77895 1.2838 .78891 5 56 089 173 .3303 934 4 56 474 941 .2830 873 4 57 112 219 .3295 916 3 57 497 .77988 .2822 855 3 58 135 264 .3287 899 2 58 520 .78035 .2815 837 2 59 158 310 .3278 881 1 59 543 082 .2807 819 1 60 .60182 .75355 1.3270 .79864 60 .61566 .78129 1.2799 .78801 _0_ Cos Ctn Tan Sin / Cos Ctn Tan Sin / 53 C 52 C II] 38 Values of Trigonometric Functions 39 C 41 / Sin Tan Ctn Cos / Sin Tan Ctn Cos .61566 .78129 1.2799 .78801 60 .62932 .80978 1.2349 .77715 60 1 589 175 .2792 783 59 1 955 .81027 .2342 696 59 2 612 222 .2784 765 58 2 .62977 075 .2334 678 58 3 635 269 .2776 747 57 3 .63000 123 .2327 660 57 4 658 316 .2769 729 56 4 022 171 .2320 641 56 5 .61681 .78363 1.2761 .78711 55 5 .63045 .81220 1.2312 .77623 55 6 704 410 .2753 694 54 6 068 268 .2305 605 54 7 726 457 .2746 676 53 7 090 316 .2298 586 53 8 749 504 .2738 658 52 -s 113 364 .2290 568 52 9 772 551 .2731 640 51 9 135 413 .2283 550 51 10 .61795 .78598 1.2723 .78622 50 10 .63158 .81461 1.2276 .77531 50 11 818 645 .2715 604 49 11 180 510 .2268 513 49 12 841 692 .2708 586 48 12 203 558 .2261 494 48 13 864 739 .2700 568 47 13 225 606 .2254 476 47 14 887 786 .2693 550 46 14 248 655 .2247 458 46 15 .61909 .78834 1.2685 .78532 45 15 .63271 .81703 1.2239 .77439 45 16 932 881 .2677 514 44 16 293 752 .2232 421 44 17 955 928 .2670 496 43 17 316 800 .2225 402 43 18 .61978 .78975 .2662 478 42 18 338 849 .2218 384 42 19 .62001 .79022 .2655 460 41 19 361 898 .2210 366 41 20 .62024 .79070 1.2647 .78442 40 20 .63383 .81946 1.2203 .77347 40 21 046 117 .2640 424 39 21 406 .81995 .2196 329 39 22 069 164 .2632 405 38 22 428 .82044 .2189 310 38 23 092 212 .2624 387 37 23 451 092 .2181 292 37 24 115 259 .2617 369 36 24 473 141 .2174 273 36 25 .62138 .79306 1.2609 .73351 35 25 .63496 .82190 1.2167 .77255 35 26 160 354 .2602 333 34 26 518 238 .2160 236 34 27 183 401 .2594 315 33 27 540 287 .2153 218 33 28 206 449 .2587 297 32 28 563 336 .2145 199 32 29 229 496 .2579 279 31 29 585 385 .2138 181 31 30 .62251 .79544 1.2572 .78261 30 30 .63608 .82434 1.2131 .77162 30 31 274 591 .2564 243 29 31 630 483 .2124 144 29 32 297 639 .2557 225 28 32 653 531 .2117 125 28 33 320 686 .2549 206 27 33 675 580 .2109 107 27 34 342 734 .2542 188 26 34 698 629 .2102 088 26 35 .62365 .79781 1.2534 .78170 25 35 .63720 .82678 1.2095 .77070 25 36 -388 829 .2527 152 24 36 742 727 .2088 051 24 37 411 877 .2519 134 23 37 765 776 .2081 033 23 38 433 924 .2512 116 22 38 787 825 .2074 .77014 22 39 456 .79972 .2504 098 21 39 810 874 .2066 .76996 21 40 .62479 .80020 1.2497 .78079 20 40 .63832 .82923 1.2059 .76977 20 41 502 067 .2489 061 19 41 854 .82972 .2052 959 19 42 524 115 .2482 043 18 42 877 .83022 .2045 940 18 43 547 163 .2475 025 17 43 899 071 .2038 921 17 44 570 211 .2467 .78007 16 44 922 120 .2031 903 16 45 .62592 .80258 1.2460 .77988 15 45 .63944 .83169 1.2024 .76884 15 46 615 306 .2452 970 14 46 966 218 .2017 866 14 47 638 354 .2445 952 13 47 .63989 268 .2009 847 13 48 660 402 .2437 934 12 48 .64011 317 .2002 828 12 49 683 450 .2430 916 11 49 033 366 .1995 810 11 50 .62706 .80498 1.2423 .77897 10 50 .64056 .83415 1.1988 .76791 10 51 728 546 .2415 879 9 51 078 465 .1981 772 9 52 751 594 .2408 861 8 52 100 514 .1974 754 8 53 774 642 .2401 843 7 53 123 564 .1967 735 7 54 796 690 .2393 824 6 54 145 613 .1960 717 6 55 .62819 .80738 1.2386 .77806 5 55 .64167 .83662 1.1953 .76698 5 56 842 786 .2378 788 4 56 190 712 .1946 679 4 57 864 834 .2371 769 3 57 212 761 .1939 661 3 58 887 882 .2364 751 2 58 234 811 .1932 642 2 59 909 930 .2356 733 1 59 256 860 .1925 623 1 60 .62932 .80978 1.2349 .77715 60 .64279 .83910 1.1918 .76604 Cos Ctn Tan Sin ' Cos Ctn Tan Sin ' 51 C 50 C 42 40 Values of Trigonometric Functions 41 C [II / Sin Tan Ctn Cos 1 Sin Tan Ctn Cos .64279 .83910 1.1918 .76604 60 .65606 .86929 1.1504 .75471 60 1 301 .83960 .1910 586 59 1 628 .86980 .1497 452 59 2 323 .84009 .1903 567 58 2 650 .87031 .1490 433 58 3 346 059 .1896 548 57 3 672 082 .1483 414 57 4 368 108 .1889 530 56 4 694 133 .1477 395 56 5 .64390 .84158 1.1882 .76511 55 5 .65716 .87184 1.1470 .75375 55 6 412 208 .1875 492 54 6 738 236 .1463 356 54 7 435 258 .1868 473 53 7 759 287 .1456 337 53 8 457 307 .1861 455 52 8 781 338 .1450 318 52 9 479 357 .1854 436 51 9 803 389 .1443 299 51 10 .64501 .84407 1.1847 .76417 50 10 .65825 .87441 1.1436 .75280 50 11 524 457 .1840 398 49 11 847 492 .1430 261 49 12 546 507 .1833 380 48 12 869 543 .1423 241 48 13 568 556 .1826 361 47 13 891 595 .1416 222 47 14 590 606 .1819 342 46 14 913 646 .1410 203 46 15 .64612 .84656 1.1812 .76323 45 15 .65935 .87698 1.1403 .75184 45 16 635 706 .1806 304 44 16 956 749 .1396 165 44 17 657 756 .1799 286 43 17 .65978 801 .1389 146 43 18 679 806 .1792 267 42 18 .66000 852 .1383 126 42 19 701 856 .1785 248 41 19 022 904 .1376 107 41 20 .64723 .84906 1.1778 .76229 40 20 .66044 .87955 1.1369 .75088 40 21 746 .84956 .1771 210 39 21 066 .88007 .1363 069 39 22 768 .85006 .1764 192 38 22 088 059 .1356 050 38 23 790 057 .1757 173 37 23 109 110 .1349 030 37 24 812 107 .1750 154 36 24 131 162 .1343 .75011 36 25 .64834 .85157 1.1743 .76135 35 25 .66153 .88214 1.1336 .74992 35 26 856 207 .1736 116 34 26 175 265 .1329 973 34 27 878 257 .1729 097 33 27 197 317 .1323 953 33 28 901 308 .1722 078 32 28 218 369 .1316 934 32 29 923 358 .1715 059 31 29 240 421 .1310 915 31 30 64945 .85408 1.1708 .76041 30 30 .66262 .88473 1.1303 .74896 30 31 967 458 .1702 022 29 31 284 524 .1296 876 29 32 .64989 509 .1695 .76003 28 32 306 576 .1290 857 28 33 .65011 559 .1688 .75984 27 33 327 628 .1283 838 27 34 033 609 .1681 965 26 34 349 680 .1276 818 26 35 .65055 .85660 1.1674 .75946 25 35 .66371 .88732 1.1270 .74799 25 36 077 710 .1667 927 24 36 393 784 .1263 780 24 37 100 761 .1660 908 23 37 414 836 .1257 760 23 38 122 811 .1653 889 22 38 436 888 .1250 741 22 39 144 862 .1647 870 21 39 458 940 .1243 722 21 40 .65166 .85912 1.1640 .75851 20 40 .66480 .88992 1.1237 .74703 20 41 188 .85963 .1633 832 19 41 501 .89045 .1230 683 19 42 210 .86014 .1626 813 18 42 523 097 .1224 664 18 43 232 064 .1619 794 17 43 545 149 .1217 644 17 44 254 115 .1612 775 16 44 566 201 .1211 625 16 45 .65276 .86166 1.1606 .75756 15 45 .66588 .89253 1.1204 .74606 15 46 298 216 .1599 738 14 46 610 306 .1197 586 14 47 320 267 .1592 719 13 47 632 358 .1191 567 13 48 342 318 .1585 700 12 48 653 410 .1184 548 12 49 364 368 .1578 680 11 49 675 463 .1178 528 11 50 .65386 .86419 1.1571 .75661 10 50 .66697 .89515 1.1171 .74509 10 51 408 470 .1565 642 9 51 718 567 .1165 489 9 52 430 521 .1558 623 8 52 740 620 .1158 470 8 53 452 572 .1551 604 7 53 762 672 .1152 451 7 54 474 623 .1544 585 6 54 783 725 .1145 431 6 55 .65496 .86674 1.1538 .75566 5 55 .66805 .89777 1.1139 .74412 5 56 518 725 .1531 547 4 56 827 830 .1132 392 4 57 540 776 .1524 528 3 57 848 883 .1126 373 3 58 562 827 .1517 509 2 58 870 935 .1119 353 2 59 584 878 .1510 490 1 59 891 .89988 .1113 334 1 60 .65606 .86929 1.1504 .75471 60 .66913 .90040 1.1106 .74314 Cos Ctn Tan Sin 1 Cos Ctn Tan Sin / 49 C 48 C II] 42 Values of Trigonometric Functions 43 C 43 / Sin Tan Ctn Cos ' Sin Tan Ctn Cos .66913 .90040 1.1106 .74314 60 .68200 .93252 1.0724 .73135 60 1 935 093 .1100 295 59 1 221 306 .0717 116 59 2 956 146 .1093 276 58 2 242 360 .0711 096 58 3 978 199 .1087 256 57 3 264 415 .0705 076 57 4 .66999 251 .1080 237 56 4 285 469 .0699 056 56 5 .67021 .90304 1.1074 .74217 55 5 .68306 .93524 1.0692 .73036 55 6 043 357 .1067 198 54 6 327 578 .0686 .73016 54 7 064 410 .1061 178 53 7 349 633 .0680 .72996 53 8 086 463 .1054 159 52 8 370 688 .0674 976 52 9 107 516 .1048 139 51 9 391 742 .0668 957 51 10 .67129 .90569 1.1041 .74120 50 10 .68412 .93797 1.0661 .72937 50 11 151 621 .1035 100 49 11 434 oC^ .0655 917 49 12 172 674 .1028 080 48 12 455 906 .0649 897 48 13 194 727 .1022 061 47 13 476 .93901 .0643 877 47 14 215 781 .1016 041 46 14 497 .94016 .0637 857 46 15 .67237 .90834 1.1009 .74022 45 15 .68518 .94071 1.0630 .72837 45 16 258 887 .1003 .74002 44 16 539 125 .0624 817 44 17 280 940 .0996 .73983 43 17 561 180 .0618 797 43 18 301 .90993 .0990 963 42 18 582 235 .0612 777 42 19 323 .91046 .0983 944 41 19 603 290 .0606 757 41 20 .67344 .91099 1.0977 .73924 40 20 .68624 .94345 1.0599 .72737 40 21 366 153 .0971 904 39 21 645 400 .0593 717 39 22 387 206 .0964 885 38 22 666 455 .0587 697 38 23 409 259 .0958 865 37 23 688 510 .0581 677 37 24 430 313 .0951 846 36 24 709 565 .0575 657 36 25 .67452 .91366 1.0945 .73826 35 25 .68730 .94620 1.0569 .72637 35 26 473 419 .0939 806 34 26 751 676 .0562 617 34 27 495 473 .0932 787 33 27 772 731 .0556 597 33 28 516 526 .0926 767 32 28 793 786 .0550 577 32 29 538 580 .0919 747 31 29 814 841 .0544 557 31 30 .67559 .91633 1.0913 .73728 30 30 .68835 .94896 1.0538 .72537 30 31 580 687 .0907 708 29 31 857 .94952 .0532 517 29 32 602 740 .0900 688 28 32 878 .95007 .0526 497 28 33 623 794 .0894 669 27 33 899 062 .0519 477 27 34 645 847 .0888 649 26 34 920 118 .0513 457 26 35 .67666 .91901 1.0881 .73629 25 35 .68941 .95173 1.0507 .72437 25 36 688 .91955 .0875 610 24 36 962 229 .0501 417 24 37 709 .92008 .0869 590 23 37 .68983 284 .0495 397 23 38 730 062 .0862 570 22 38 .69004 340 .0489 377 22 39 752 116 .0856 551 21 39 025 395 .0483 357 21 40 .67773 .92170 1.0850 .73531 20 40 .69046 .95451 1.0477 .72337 20 41 795 224 .0843 511 19 41 067 506 .0470 317 19 42 816 277 .0837 491 18 42 088 562 .0464 297 18 43 837 331 .0831 472 17 43 109 618 .0458 277 17 44 859 385 .0824 452 16 44 130 673 -0452 257 16 45 .67880 .92439 1.0818 .73432 15 45 .69151 .95729 1.0446 .72236 15 46 901 493 .0812 4J J4 46 172 785 .0440 216 14 47 923 547 .0805 393 13 47 193 841 .0434 196 13 48 944 601 .0799 37? 12 48 214 897 .0428 176 12 49 965 655 .0793 353 11 49 235 .95952 .0422 156 11 50 .67987 .92709 1.0786 .73333 10 50 .69256 .96008 1.0416 .72136 10 51 .68008 763 .0780 314 9 51 277 064 .0410 116 9 52 029 817 .0774 294 8 52 298 120 .0404 095 8 53 051 872 .0768 274 7 53 319 176 .0398 075 7 54 072 926 .0761 254 6 54 340 232 .0392 055 6 55 .68093 .92980 1.0755 .73234 5 55 .69361 .96288 1.0385 .72035 5 56 115 .93034 .0749 215 4 56 382 344 .0379 .72015 4 57 136 088 .0742 195 3 57 403 400 .0373 .71995 3 58 157 143 .0736 175 2 58 424 457 .0367 974 2 59 179 197 .0730 155 1 59 445 513 .0361 954 1 60 .68200 .93252 1.0724 .73135 60 .69466 .96569 1.0355 .71934 Cos Ctn Tan Sin / Cos Ctn Tan Sin / 47 C 46 C 44 44 Values of Trigonometric Functions 1 Sin Tan Ctn Cos .69466 .96569 1.0355 .71934 60 1 487 625 .0349 914 59 2 508 681 .0343 894 58 3 529 738 .0337 873 57 4 549 794 .0331 853 56 5 .69570 .96850 1.0325 .71833 55 6 591 907 .0319 813 54 7 612 .96963 .0313 792 53 8 633 .97020 .0307 111 52 9 654 076 .0301 752 51 10 .69675 .97133 1.0295 .71732 50 11 696 189 .0289 711 49 12 717 246 .0283 691 48 13 737 302 .0277 671 47 14 758 359 .0271 650 46 15 .69779 .97416 1.0265 .71630 45 16 800 472 .0259 610 44 17 821 529 .0253 590 43 18 842 586 .0247 569 42 19 862 643 .0241 549 41 20 .69883 .97700 1.0235 .71529 40 21 904 756 .0230 508 39 22 925 813 .0224 488 38 23 946 870 .0218 468 37 24 966 927 .0212 447 36 25 .69987 .97984 1.0206 .71427 35 26 .70008 .98041 .0200 407 34 27 029 098 .0194 386 33 28 049 155 .0188 366 32 29 070 213 .0182 345 31 30 .70091 .98270 1.0176 .71325 30 31 112 327 .0170 305 29 32 132 384 .0164 284 28 33 153 441 .0158 264 27 34 174 499 .0152 243 26 35 .70195 .98556 1.0147 .71223 25 36 215 613 .0141 203 24 37 236 671 .0135 182 23 38 257 728 .0129 162 22 39 277 786 .0123 141 21 40 .70298 .98843 1.0117 .71121 20 41 319 901 .0111 100 19 42 339 .98958 .0105 080 18 43 360 .99016 .0099 059 17 44 381 073 .0094 039 16 45 .70401 .99131 1.0088 .71019 15 46 422 189 .0082 .70998 14 47 443 247 .0076 978 13 48 463 304 .0070 957 12 49 484 362 .0064 937 11 50 .70505 .99420 1.0058 .70916 10 51 525 478 .0052 896 52 546 536 .0047 875 8 53 567 594 .0041 855 7 54 587 652 .0035 834 6 55 .70608 .99710 1.0029 .70813 5 56 628 768 .0023 793 4 57 649 826 .0017 772 3 58 670 884 .0012 752 2 59 690 .99942 .0006 731 1 60 .70711 1.0000 1.0000 .70711 Cos Ctn Tan Sin / 45 C TABLE IH COMMON LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS FROM TO 90 AT INTERVALS OF ONE MINUTE TO FIVE DECIMAL PLACES From each logarithm given, subtract 10 Table Ilia Auxiliary Table of S and T for A in Minutes S = log sin A log A' and T = log tan A log A' A' S+10 0' - 13' 6.46373 14' - 42' 72 43' - 58' 71 59' - 71' 6.46370 72' - 81' 69 82' - 91' 68 92' - 99' 6.46367 100' - 107' 66 108' - 115' 65 116' - 121' 6.46364 122' 128' 63 129' - 134' 62 135' - 140' 6.46361 141' - 146' 60 147' - 151' 59 152' - 157' 6.46358 158' - 162' 57 163' - 167' 56 168' - 171' 6.46355 172' - 176' 54 177' - 181' 53 A 1 r+io 0' - 26' 6.46373 27' - 39' 74 40' - 48' 75 49' - 56' 6.46376 57' - 63' 77 64' - 69' 78 70' - 74' 6.46379 75' - 80' 80 81' - 85' 81 86' - 89' 6.46382 90' - 94' 83 95' - 98' 84 99' - 102' 6.46385 103' - 106' 86 107' - 110' 87 111' - 113' 6.46388 114' - 117' 89 118' - 120' 90 121' - 124' 6.46391 125' - 127' 92 128' - 130' 93 A' T+10 131' - 133' 6.46394 134' - 136' 95 137' - 139' 96 140' - 142' 6.46397 143' - 145' 98 146' - 148' 99 149' - 150' 6.46400 151' - 153' 01 154' - 156' 02 157' - 158' 6.46403 159' - 161' 04 162' - 163' 05 164' - 166' 6.46406 167' - 168' 07 169' - 171' 08 172' - 173' 6.46409 174' - 175' 10 176' - 178' 11 179' - 180' 6.46412 181' - 182' 13 183' - 184' 14 For small angles: log sin A = log A' + S and log tan A = log A' + T. For angles near 90: log cos A = log (90 - A)' + S, log ctn A = log (90 - A)' + T where A' = number of minutes in A, and (90 A)' = number of minutes in 90 - A. 45 46 Logarithms of Trigonometric Functions ' LSin d LTan cd LCtn L Cos in on nnn fin 1 6.46 373 6.46 373 13.53 627 AV.Ul/ v/UU 10.00 000 DU 59 2 6.76 476 30103 6.76 476 30103 13.23 524 10.00 000 58 3 6.94 085 17609 6.94 085 17609 13.05 915 10.00 000 57 4 7.06 579 12494 7.06 579 12494 12.93 421 10.00 000 56 5 7.16 270 9691 7.16270 9691 12.83 730 10.00 000 55 6 7.24 188 7918 7.24 188 7918 12.75 812 10.00 000 54 7 7.30 882 6694 7.30 882 6694 12.69 118 10.00 000 53 8 7.36 682 5800 7.36 682 5800 12.63 318 10.00 000 52 9 7.41 797 5115 7.41 797 5115 12.58 203 10.00 000 51 o ||| 10 7.46 373 7.46 373 12.53 627 10.00 000 50 11 7.50 512 4139 7.50512 4139 12.49 488 10.00 000 49 S bD 3 12 7.54 291 3779 7.54 291 3779 12.45 709 10.00 000 48 ^ . . fl .2 13 7.57 767 3476 7.57 767 3476 12.42 233 10.00 000 47 'C 52 ^ J* f^ 14 7.60 985 3218 7.60 986 3219 12.39 014 10.00 000 46 -fr 3 fe O 15 7.63 982 2997 7.63 982 2996 12.36 018 10.00 000 45 ^^ ** '" 16 7.66 784 2802 7.66 785 2803 12.33 215 10.00 000 44 t- cf >> ^ "3 17 7.69 417 2633 7.69 418 2633 12.30 582 9.99 999 43 O * 1 3 "H ^ 18 7.71 900 2483 7.71 900 2482 12.28 100 9.99 999 42 ^"'K 3 Jfi o3 19 7.74 248 2348 7.74 248 2348 12.25 752 9.99 999 41 co o> M 3 "t5 20 7.76 475 2227 7.76 476 2228 12.23 524 9.99 999 40 e) 3 ^ w 21 7.78 594 2119 7.78 595 2119 12.21 405 9.99 999 39 r-j C-i ''"', t-> O 22 7.80 615 2021 7.80 615 2020 12.19385 9.99 999 38 23 7.82 545 1930 7.82 546 1931 12.17 454 9.99 999 37 W ^ j3 (D O 24 7.84 393 1848 7.84 394 1848 12.15 606 9.99 999 36 V w ~S 3 -5 25 7.86 166 1773 7.86 167 1773 12.13 833 9.99 999 35 11 ^ fl -3 26 7.87 870 1704 7.87 871 1704 12.12 129 9.99 999 34 ?-. +3 03 27 7.89 509 1639 7.89 510 1639 12.10490 9.99 999 33 5P 03 2 IS ^ 28 7.91 088 1579 7.91 089 1579 12.08911 9.99 999 32 M r* f^ * tn o3 5 -^ o3 29 7.92 612 1524 7.92 613 1524 12.07 387 9.99 998 31 * -. 3 c 30 7.94 084 1472 7.94 086 1473 12.05 914 9.99 998 30 o -^> 6* 9 ^,0 f t 31 7.95 508 1424 7.95 510 1424 12.04 490 9.99 998 29 -*j> Q) o3 CN Q 32 7.96 887 1379 7.96 889 1379 12.03 111 9.99 998 28 ~c3 "o "^ 33 7.98 223 1336 7.98 225 1336 12.01 775 9.99 998 27 bC O> < 2 t^ 34 7.99 620 1297 7.99 522 1297 12.00 478 9.99 998 26 2 Sb 14- 35 8.00 779 1259 8.00 781 1259 11.99219 9.99 998 25 ^ O .1^ 36 8.02 002 1223 8.02 004 1223 11.97996 9.99 998 24 o "Eb ^ ^ ^ 37 8.03 192 1190 8.03 194 1190 11.96806 9.99 997 23 M t-t *t-t gj 38 8.04 350 1158 8.04 353 1159 11.95 647 9.99 997 22 39 8.05 478 1128 8.05 481 1128 11.94519 9.99 997 21 9 *g 3 119'.0 118.3 21 8.87 995 166 8.88 120 167 11.11880 9.99 875 39 8 136.8 136.0 135.2 22 8.88 161 166 8.88 287 167 11.11713 9.99 874 38 9 153.9 153.0 152.1 23 8.88 326 165 8.88 453 166 11.11547 9.99 873 37 1 AT 1AR 1AQ 24 8.88 490 164 164 8.88 618 165 165 11.11382 9.99 872 36 2 33.4 33.0 32.6 25 8.88 654 8.88 783 11.11217 9.99 871 35 3 50.1 49.5 48.9 26 8.88 817 163 8.88 948 165 11.11052 9.99 870 34 4 5 66.8 66.0 65.2 835 825 81.5 27 8.88 980 163 8.89 111 163 11.10889 9.99 869 33 6 100.2 99.0 97.8 28 29 8.89 142 8.89 304 162 162 8.89 274 8.89 437 163 163 11.10726 11.10663 9.99 868 9.99 867 32 31 7 8 9 116.9 115.5 114.1 133.6 132.0 130.4 150.3 148.5 146.7 30 8.89 464 160 8.89 598 161 11.10402 9.99 866 30 31 8.89 625 161 8.89 760 162 11.10240 9.99 865 29 161 160 169 32 33 8.89 784 8.89 943 159 159 8.89 920 8.90 080 160 160 11.10080 11.09920 9.99 864 9.99 863 28 27 2 3 4 32.2 32.0 31.8 48.3 48.0 47.7 64.4 64.0 63.6 34 8.90 102 159 8.90 240 160 11.09760 9.99 862 26 5 80.5 80.0 79.5 158 159 6 96 6 96 95 4 35 8.90 260 8.90 399 11.09601 9.99 861 25 7 112> 112.0 111.3 36 37 8.90417 8.90 574 157 157 8.90 557 8.90 715 158 158 11.09443 11.09 285 9.99 860 9.99 859 24 23 8 9 128.8 128.0 127.2 144.9 144.0 143.1 38 8.90 730 156 8.90 872 157 11.09 128 9.99 858 22 1 K7 1KB 1 K9 39 8.90 885 155 155 8.91 029 157 156 11.08971 9.99 857 21 2 31.4 31.0 30.6 40 8.91 040 8.91 185 11.08815 9.99 856 20 3 47.1 46.5 45.9 41 8.91 195 155 8.91 340 155 11.08660 9.99 855 19 4 5 62.8 62.0 61.2 78.5 77.5 76.5 42 8.91 349 154 8.91 495 155 11.08505 9.99 854 18 6 94.2 93.0 91.8 43 8.91 502 153 8.91 650 155 11.08350 9.99 853 17 7 g 109.9 108.5 107.1 125 A 124 122 4 44 8.91 655 153 8.91 803 153 11.08197 9.99 852 16 9 141u 139^5 137.'7 45 8.91 807 152 8.91 957 154 11.08 043 9.99 851 15 46 8.91 959 152 8.92 110 153 11.07890 9.99 850 14 151 150 149 47 8.92 110 151 8.92 262 152 11.07738 9.99 848 13 2 3 30.2 30.0 29.8 45 3 45 44 7 48 8.92 261 151 8.92 414 152 11.07586 9.99 847 12 4 60^4 60'.0 59'.6 49 8.92411 150 8.92 565 151 11.07435 9.99 846 11 5 75.5 75.0 74.5 150 151 6 90.6 90.0 89.4 50 8.92 561 8.92 716 11.07284 9.99 845 10 7 105.7 105.0 104.3 51 52 8.92 710 8.92 859 149 149 8.92 866 8.93 016 150 150 11.07 134 11.06984 9.99 844 9.99 843 9 8 8 9 120.8 120.0 119.2 135.9 135.0 134.1 53 8.93 007 148 8.93 165 149 11.06835 9.99842. 7 147 145 144 54 8.93 154 147 14.7 8.93 313 148 1 4.Q 11.06687 9.99 841 6 2 29.4 29.0 28.8 55 8.93 301 XT:/ 8.93 462 J.*<7 11.06538 9.99 840 5 3 44.1 43.5 43.2 56 8.93 448 147 8.93 609 147 11.06391 9.99 839 4 4 5 58.8 58.0 57.6 73.5 72.5 72.0 57 8.93 594 146 8.93 756 147 11.06244 9.99 838 3 6 88.2 87.0 86.4 58 8.93 740 146 8.93 903 147 11.06097 9.99 837 2 7 g 102.9 101.5 100.8 117 6 116 115 2 59 8.93 885 145 145 8.94 049 146 146 11.05951 9.99 836 1 9 132'.3 130'.5 129.6 60 8.94 030 8.94 195 11.05805 9.99 834 LCos d LCtn cd LTan LSin ' Prop. Pts. 85 Logarithms of Trigonometric Functions Ill] 5 Logarithms of Trigonometric Functions 51 ' LSin d LTan cd LCtn L Cos Prop. Pts. 8.94 030 8.94 195 11.05805 9.99 834 60 1 8.94 174 144 8.94 340 145 11.05 660 9.99 833 59 143 142 141 2 8.94 317 143 8.94 485 145 11.05515 9.99 832 58 2 28.6 28.4 28.2 3 8.94 461 144 8.94 630 145 11.05370 9.99 831 57 3 4 42.9 42.6 42.3 57.2 56.8 56.4 4 8.94 603 142 8.94 773 143 11.05 227 9.99 830 56 5 71.5 71.0 70.5 143 144 6 85 8 85 2 84 6 5 8.94 746 8.94 917 11.05083 9.99 829 55 7 100.1 99i4 98'.7 6 8.94 887 141 8.95 060 143 11.04940 9.99 828 54 8 114.4 113.6 112.8 7 8.95 029 142 8.95 202 142 11.04798 9.99 827 53 9 128.7 127.8 126.9 8 8.95 170 141 8.95 344 142 11.04 656 9.99 825 52 9 8.95 310 140 140 8.95 486 142 141 11.04514 9.99 824 51 2 UW J.03 J..SO 28.0 27.8 27.6 10 8.95 450 8.95 627 11.04 373 9.99 823 50 3 42.0 41.7 41.4 11 8.95 589 139 8.95 767 140 11.04233 9.99 822 49 4 5 56.0 55.6 55.2 70 69 5 69 12 8.95 728 139 8.95 908 141 11.04092 9.99 821 48 6 84.0 83i4 82^8 13 14 8.95 867 8.96 005 139 138 138 8.96 047 8.96 187 139 140 138 11.03 953 11.03 813 9.99 820 9.99 819 47 46 7 8 9 98.0 97.3 96.6 112.0 111.2 110.4 126.0 125.1 124.2 15 8.96 143 8.96 325 11.03 675 9.99 817 45 16 8.96 280 137 8.96 464 139 11.03 536 9.99 816 44 137 136 135 17 8.96 417 137 8.96 602 138 11.03 398 9.99 815 43 2 3 tl.t Z/.Z ZY.U 41.1 40 8 40 5 18 8.96 553 136 8.96 739 137 11.03 261 9.99 814 42 4 54.8 54.4 54.0 19 8.96 689 136 136 8.96 877 138 136 11.03 123 9.99 813 41 5 6 68.5 68.0 67.5 82.2 81.6 81.0 20 8.96 825 8.97 013 11.02 987 9.99 812 40 7 95.9 95.2 94.5 21 22 8.96 960 8.97 095 135 135 8.97 150 8.97 285 137 135 11.02850 11.02715 9.99 810 9.99 809 39 38 8 9 109.6 108.8 108.0 123.3 122.4 121.5 23 8.97 229 134 8.97 421 136 11.02579 9.99 808 37 134 133 132 24 8.97 363 134 8.97 556 135 11.02444 9.99 807 36 2 26.8 26.6 26.4 25 26 8.97 496 8.97 629 133 8.97 691 8.97 825 135 134 11.02 309 11.02175 9.99 806 9.99 804 35 34 3 4 5 40.2 39.9 39.6 53.6 53.2 52.8 67.0 66.5 66.0 27 8.97 762 133 8.97 959 134 11.02041 9.99 803 33 6 80.4 79.8 79.2 28 8.97 894 132 8.98 092 133 11.01 908 9.99 802 32 7 8 93.8 93.1 92.4 107.2 106 4 105 6 29 8.98 026 132 131 8.98 225 133 133 11.01 775 9.99 801 31 9 120.6 119.7 118.8 30 8.98 157 8.98 358 11.01 642 9.99 800 30 31 8.98 288 131 8.98 490 132 11.01510 9.99 798 29 131 130 129 32 8.98 419 131 8.98 622 132 11.01 378 9.99 797 28 2 3 ZO.Z 26.U Z5.8 39 3 39 38 7 33 8.98 549 130 8.98 753 131 11.01 247 9.99 796 27 4 52 A 52.Q 51>> 34 8.98 679 130 8.98 884 131 11.01 116 9.99 795 26 5 g 65.5 65.0 64.5 78.6 78 77 4 35 8.98 808 8.99 015 11.00985 9.99 793 25 7 9l!7 9l!o 90!3 36 37 8.98 937 8.99 066 129 129 8.99 145 8.99 275 130 130 11.00855 11.00725 9.99 792 9.99 791 24 23 8 9 104.8 104.0 103.2 117.9 117.0 116.1 38 8.99 194 128 8.99 405 130 11.00595 9.99 790 22 1S 197 19.R 39 8.99 322 128 128 8.99 534 129 11.00466 9.99 788 21 2 25.6 25.4 25.2 40 41 8.99 450 8.99 577 127 8.99 662 8.99 791 129 11.00 338 11.00209 9.99 787 9.99 786 20 19 3 4 5 38.4 38.1 37.8 51.2 50.8 50.4 64.0 63.5 63.0 42 8.99 704 127 8.99 919 128 11.00081 9.99 785 18 6 76.8 76.2 75.6 43 44 8.99 830 8.99 956 126 126 126 9.00 046 9.00 174 127 128 127 10.99 954 10.99 826 9.99 783 9.99 782 17 16 7 8 9 89.6 88.9 88.2 102.4 101.6 100.8 115.2 114.3 113.4 45 9.00 082 9.00 301 10.99 699 9.99 781 15 46 9.00 207 125 9.00 427 126 10.99 573 9.99 780 14 126 124 123 47 48 9.00 332 9.00 456 125 124 9.00 553 9.00 679 126 126 10.99 447 10.99 321 9.99 778 9.99 777 13 12 2 3 4 25.0 24.8 24.6 37.5 37.2 36.9 50.0 49.6 49.2 49 9.00 581 125 123 9.00 805 126 10.99 195 9.99 776 11 5 6 62.5 62.0 61.5 75.0 74.4 73.8 50 9.00 704 9.00 930 10.99 070 9.99 775 10 87.5 86.8 86.1 51 52 9.00 828 9.00 951 124 123 9.01 055 9.01 179 125 124 10.98 945 10.98 821 9.99 773 9.99 772 9 8 8 9 100.0 99.2 98.4 112.5 111.6 110.7 53 9.01 074 123 9.01 303 124 10.98 697 9.99771 7 195 151 15 54 9.01 196 122 122 9.01 427 124 123 10.98 573 9.99 769 6 2 24.4 24.2 24.0 55 56 9.01 318 9.01 440 122 9.01 550 9.01 673 123 10.98 450 10.98 327 9.99 768 9.99 767 5 4 3 4 5 36.6 36.3 36.0 48.8 48.4 48.0 61.0 60.5 60.0 57 9.01 561 121 9.01 796 123 10.98 204 9.99 765 3 6 73.2 72.6 72.0 58 9.01 682 121 9.01 918 122 10.98 082 9.99 764 2 7 85.4 84.7 84.0 97 6 96 8 96 59 9.01 803 121 9.02 040 122 10.97 960 9.99 763 1 9 109'.8 108'.9 108.0 60 9.01 923 9.02 162 122 10.97 838 9.99 761 LCos d LCtn cd L Tan LSin ' Prop. Pts. 84 Logarithms of Trigonometric Functions 52 6 Logarithms of Trigonometric Functions [III ' LSin d LTan cd LCtn LCos Prop. Pts. 9.01 923 9.02 162 10.97 838 9.99 761 60 1 9.02 043 120 9.02 283 121 10.97717 9.99 760 59 121 120 119 2 9.02 163 120 9.02 404 121 10.97 596 9.99 759 58 3 24.2 24. U 23.8 36.3 36.0 35.7 3 9.02 283 120 9.02 525 121 10.97 475 9.99 757 57 4 48.4 48.0 47.6 4 9.02 402 119 1 1 Q 9.02 645 120 10.97 355 9.99 756 56 a 6 60.5 60.0 59.5 72.6 72.0 71.4 5 9.02 520 llo 9.02 766 10.97 234 9.99 755 55 7 6 9.02 639 119 9.02 885 119 10.97 115 9.99 753 54 8 9 96!8 96.0 95.2 ins a ins n in? i 7 9.02 757 118 9.03 005 120 10.96 995 9.99 752 53 8 9.02 874 117 9.03 124 119 10.96 876 9.99 751 52 11H 117 11A 9 9.02 992 118 117 9.03 242 118 119 10.96 758 9.99 749 51 2 23.6 23.4 23.2 10 9.03 109 9.03 361 10.96 639 9.99 748 50 3 35.4 35.1 34.8 11 9.03 226 117 9.03 479 118 10.96 521 9.99 747 49 4 47.2 46.8 46.4 59.0 58.5 58.0 12 9.03 342 116 9.03 597 118 10.96 403 9.99 745 48 6 70.8 70.2 69.6 13 9.03 458 116 9.03 714 117 10.96 286 9.99 744 47 7 8 82.6 81.9 81.2 94.4 93.6 92.8 14 9.03 74 116 9.03 832 118 10.96 168 9.99 742 46 9 106.2 10513 104!4 15 9.03 690 116 9.03 948 116 10.96 052 9.99 741 45 16 9.03 805 115 9.04 065 117 10.95 935 9.99 740 44 116 114 113 17 9.03 920 115 9.04 181 116 10.95 819 9.99 738 43 2 23.0 22.8 22.6 18 9.04 034 114 9.04 297 116 10.95 703 9.99 737 42 3 4 34.5 34.2 33.9 46 45 6 45 2 19 9.04 149 115 9.04 413 116 10.95 587 9.99 736 41 5 57.5 57.0 56.5 20 9.04 262 113 9.04 528 115 10.95 472 9.99 734 40 6 7 69.0 68.4 67.8 80.5 79.8 79.1 21 9.04 376 114 9.04 643 115 10.95 357 9.99 733 39 8 92.0 91.2 90.4 22 9.04 490 114 9.04 758 115 10.95 242 9.99 731 38 9 103.5 102.6 101.7 23 9.04 603 113 9.04 873 115 10.95 127 9.99 730 37 24 9.04715 112 9.04 987 114 10.95 013 9.99 728 36 112 111 110 113 114 2 22 4 22 2 22 25 9.04 828 9.05 101 10.94 899 9.99 727 35 3 33.6 33.3 33.0 26 9.04 940 112 9.05214 113 10.94 786 9.99 726 34 4 44.8 44.4 44.0 27 9.05 052 112 9.05 328 114 10.94 672 9.99 724 33 5 6 56.0 55.5 55.0 67.2 66.6 66.0 28 9.05 164 112 9.05 441 113 10.94 559 9.99 723 32 7 78.4 77.7 77.0 29 9.05 275 111 111 9.05 553 112 113 10.94 447 9.99 721 31 8 9 89.6 88.8 88.0 100.8 99.9 99.0 30 9,05 386 9.05 666 10.94 334 9.99 720 30 31 9.05 497 111 9.05 778 112 10.94 222 9.99 718 29 109 108 107 32 9.05 607 110 9.05 890 112 10.94 110 9.99717 28 2 21.8 21.6 21.4 33 9.05 717 110 9.06 002 112 10.93 998 9.99 716 27 3 32.7 32.4 32.1 34 9.05 827 110 1 1 r\ 9.06 113 111 10.93 887 9.99 714 26 4 5 43.6 43.2 42.8 54.5 54.0 53.5 35 36 9.05 937 9.06 046 1IU 109 9.06 224 9.06 335 111 10.93 776 10.93 665 9.99 713' 9.99 711 25 24 e 7 8 65.4 64.8 64.2 76.3 75.6 74.9 87.2 86.4 85.6 37 9.06 155 109 9.06445 110 10.93 555 9.99 710 23 9 98.1 97.2 96.3 88 9.06 264 109 9.06 556 111 10.93 444 9.99 708 22 39 9.06 372 108 9.06 666 110 10.93 33t 9.99 707 21 106 105 104 40 9.06 481 109 9.06 775 109 10.93 225 9.99 705 20 2 3 21.2 21.0 20.8 31 8 31 5 31 2 41 9.06 589 108 9.06 885 110 10.93 115 9.99 704 19 4 42'.4 42io 4L6 42 9.06 696 107 9.06 994 109 10.93 006 9.99 702 18 5 53.0 52.5 62.0 43 9.06 804 108 9.07 103 109 10.92 897 9.99 701 17 6 7 63.6 63.0 62.4 74 2 73.5 72.8 44 9.06911 107 9.07211 108 10.92 789 9.99 699 16 8 84.8 84.0 83.2 45 9.07 018 107 9.07 320 109 10.92 680 9.99 698 15 9 95.4 94.5 93.6 46 47 9.07 124 9.07 231 106 107 9.07 428 9.07 536 108 108 10.92 572 10.92 464 9.99 696 9.99 695 14 13 From the top: 48 9.07 337 106 9.07 643 107 10.92 357 9.99 693 12 For 6 0+ or 186+, 49 9.07 442 105 106 9.07 751 108 107 10.92 249 9.99 692 11 read as printed; for 50 51 9.07 548 9.07 653 105 9.07 858 9.07 964 106 10.92 142 10.92 036 9.99 690 9.99 689 10 9 96 - 1 - or 276+, read 52 9.07 758 105 9.08071 107 10.91 929 9.99 687 8 co-function. 53 9.07 863 105 9.08 177 106 10.91 823 9.99 686 7 54 9.07 968 105 9.08 283 106 10.91717 9.99 684 6 From the bottom: 55 56 57 9.08 072 9.08 176 9.08 280 104 104 104 9.08 389 9.08 495 9.08 600 106 106 105 10.91 611 10.91 505 10.91 400 9.99 683 9.99 681 9.99 680 5 4 3 For 83+ or 263+ read as printed; for 58 9.08 383 103 9.08 705 105 10.91 295 9.99 678 2 173+ or 353+, read 59 9.08 486 103 103 9.08810 105 104 10.91 190 9:99-677- 1 co-function. 60 9.08 589 9.08 914 10.91 086 9.99 675 LCos d LCtn cd LTan LSin ' Prop. Pts. 83 Logarithms of Trigonometric Functions Ill] 7 Logarithms of Trigonometric Functions 53 ' LSin d L Tan cd LCtn LCos Prop. Pts. 9.08 589 9.08 914 10.91 086 9.99 675 60 1 9.08 692 103 9.09 019 105 10.90 981 9.99 674 59 2 9.08 795 103 9.09 123 104 10.90 877 9.99 672 58 105 104 103 3 9.08 897 102 9.09 227 104 10.90 773 9.99 670 57 2 21.0 20.8 20.6 4 9.08 999 102 9.09 330 103 1 A.1 10.90 670 9.99 669 56 3 4 31.5 31.2 30.9 42.0 41.6 41.2 5 9.09 101 102 9.09 434 1O1 10.90 566 9.99 667 55 5 52.5 52.0 51.5 63.0 62 4 61 8 6 9.09 202 101 9.09 537 103 10.90 463 9.99 666 54 7 73^5 72^8 72!l 7 9.09 304 102 9.09 640 103 10.90 360 9.99 664 53 8 84.0 83.2 82.4 8 9.09 405 101 9.09 742 102 10.90 258 9.99 663 52 9 94.5 93.6 92.7 9 9.09 506 101 9.09 845 103 10.90 155 9.99 661 51 10 9.09 606 100 9.09 947 102 10.90 053 9.99 659 50 102 101 99 11 9.09 707 101 9.10 049 102 1 At 10.89 951 9.99 658 49 2 20.4 20.2 19.8 12 9.09 807 100 9.10 150 1U1 10.89 850 9.99 656 48 3 30.6 30.3 29.7 13 14 9.09 907 9.10006 100 99 9.10 252 9.10 353 102 101 10.89 748 10.89 647 9.99 655 9.99 653 47 46 4 5 6 40.8 40.4 39.6 51.0 50.5 49.5 61.2 60.6 59.4 15 9.10 106 100 9.10 454 101 10.89 546 9.99 651 45 7 8 71.4 70.7 C9.3 81 6 80 8 79 2 16 9.10 205 99 9.10 555 101 10.89 445 9.99 650 44 9 91.8 90.9 89.1 17 9.10 304 99 9.10 656 101 10.89 344 9.99 648 43 18 9.10 402 98 9.10756 100 10.89 244 9.99 647 42 19 9.10501 99 9.10 856 100 10.89 144 9.99 645 41 98 97 96 20 21 9.10 599 9.10 697 98 98 9.10 956 9.11 056 100 100 10.89 044 10.88 944 9.99 643 9.99 642 40 39 2 3 4 19.6 19.4 19.2 29.4 29.1 28.8 39.2 38.8 38.4 22 9.10 795 98 9.11 155 99 10.88 845 9.99 640 38 5 49.0 48.5 48.0 23 9.10 893 98 9.11 254 99 10.88 746 9.99 638 37 6 58.8 58.2 57.6 68 6 67 9 67 2 24 9.10 990 97 9.11 353 99 10.88 647 9.99 637 36 8 78.'4 77^6 76.8 25 9.11 087 97 9.11 452 99 10.88 548 9.99 635 35 9 83.2 87.3 86.4 26 9.11 184 97 9.11551 99 10.88 449 9.99 633 34 27 9.11 281 97 9.11 649 98 10.88 351 9.99 632 33 28 9.11 377 96 9.11 747 98 10.88 253 9.99 630 32 95 94 93 29 9.11 474 97 Qfi 9.11 845 98 98 10.88 155 9.99 629 31 2 3 19.U 18.8 1S.C 28.5 28.2 27.9 30 31 9.11 570 9.11 666 *7U 96 9.11 943 9.12 040 97 10.88 057 10.87 960 9.99 627 9.99 625 30 29 4 5 6 38.0 37.6 37.2 47.5 47.0 46.5 57.0 56.4 55.8 32 9.11 761 95 9.12 138 98 10.87 862 9.99 624 28 7 66.5 65.8 65.1 33 9.11 857 96 9- 9.12 235 97 10.87 765 9.99 622 27 8 9 76.0 75.2 74.4 85.5 84.6 83.7 34 9.11 952 o 9.12 332 97 10.87 668 9.99 620 26 35 9.12 047 95 9.12 428 96 10.87 572 9.99 618 25 36 9.12 142 95 9.12 525 97 10.87 475 9.99 617 24 92 91 90 37 9.12 236 94 9.12621 96 10.87 379 9.99 615 23 2 18.4 18.2 18.0 38 39 9.12 331 9.12 425 95 94 9.12717 9.12813 96 96 OA 10.87 283 10.87 187 9.99 613 9.99 612 22 21 3 4 5 27.6 27.3 27.0 36.8 36.4 36.0 46.0 45.5 45.0 40 9.12519 94 9.12 909 yo 10.87 091 9.99 610 20 6 7 55.2 64.6 54.0 64 4 63.7 63.0 41 9.12 612 93 9.13 004 yo 10.86 996 9.99 608 19 8 73^6 72.8 72.0 42 9.12 706 94 9.13 099 95 10.86 901 9.99 607 18 9 82.8 81.9 81.0 43 9.12799 93 9.13 194 95 10.86 806 9.99 605 17 44 9.12 892 93 9.13 289 95 10.86711 9.99 603 16 45 9.12 985 93 9.13 384 95 10.86 616 9.99 601 15 From the top: 46 9.13 078 93 9.13 478 94 9e 10.86 522 9.99 600 14 For 7 0+ or 187+, 47 48 9.13 171 9.13 263 93 92 9.13 573 9.13 667 94 10.86 427 10.86 333 9.99 598 9.99 596 13 12 read as printed; for 49 9.13 355 92 9.13761 94 10.86 239 9.99 595 11 97 0+ or 277 0+ , read 50 9.13 447 92 9.13 854 93 10.86 146 9.99 593 10 co-function. 51 9.13 539 92 9.13 948 94 10.86 052 9.99 591 9 52 9.13 630 91 9.14 041 93 10.85 959 9.99 589 8 53 9.13 722 92 9.14 134 93 10.85 866 9.99 588 7 From the bottom: 54 55 56 9.13 813 9.13 904 9.13 994 91 91 90 9.14 227 9.14 320 9.14412 93 93 92 10.85 773 10.85 680 10.85 588 9.99 586 9.99 584 9.99 582 6 5 4 For 82+ or 262+, read as printed; for 57 9.14 085 91 9.14 504 92 10.85 496 9.99 581 3 172+ or 352 0+ , read 58 9.14 175 90 9.14 597 93 10.85 403 9.99 579 2 co-function. 59 9.14 266 91 9.14 688 91 10.85 312 9.99 577 1 60 9.14 356 90 9.14 780 92 10.S5 220 9.99 575 L Cos d L Ctn cd L Tan LSin ' Prop. Pts. 82 Logarithms of Trigonometric Functions 54 8 Logarithms of Trigonometric Functions [HI / LSin d LTan cd LCtn LCos Prop. Pts. 9.14 356 9.14780 10.85 220 9.99 575 60 1 9.14 445 89 9.14872 92 10.85 128 9.99 574 59 2 9.14 535 90 9.14 963 91 10.85 037 9.99 572 58 92 91 90 3 4 9.14 624 9.14714 89 90 89 9.15 054 9.15 145 91 91 91 10.84 946 10.84 855 9.99 570 9.99 568 57 56 2 3 18.4 27.6 18.2 27.3 18.0 27.0 5 9.14 803 9.15 236 10.84 764 9.99 566 55 4 36.8 36.4 36.0 6 9.14891 88 9.15 327 91 10.84 673 9.99 565 54 5 46.0 45.5 45.0 7 9.14 980 89 9.15417 90 10.84 583 9.99 563 53 6 55.2 54.6 54.0 8 9.15 069 89 9.15508 91 10.84 492 9.99 561 52 7 64.4 63.7 63.0 9 9.15 157 88 9.15 598 90 10.84 402 9.99 559 51 8 73.6 72.8 72.0 10 9.15 245 88 9.15 688 90 10.84 312 9.99 557 50 9 82.8 81.9 81.0 11 9.15 333 88 9.15 777 89 10.84 223 9.99 556 49 12 9.15421 88 9.15 867 90 10.84 133 9.99 554 48 13 9.15 508 87 9.15 956 89 10.84 044 9.99 552 47 OB 00 BY 14 9.15 596 88 9.16 046 90 10.83 954 9.99 550 46 2 17.8 17.6 17.4 15 9.15 683 87 9.16 135 89 10.83 865 9.99 648 45 3 26.7 26.4 26.1 16 9.15 770 87 9.16 224 89 10.83 776 9.99 546 44 4 35.6 35.2 34.8 17 9.15 857 87 9.16 312 88 10.83 688 9.99 545 43 5 44.5 44.0 43.5 18 9.15 944 87 9.16401 89 10.83 599 9.99 543 42 6 53.4 52.8 52.2 19 9.16 030 86 9.16 489 88 10.83511 9.99 541 41 7 62.3 61.6 60.9 86 88 8 71.2 70.4 69.6 20 9.16 116 9.16 577 10.83 423 9.99 539 40 g 80.1 79.2 78.3 21 9.16 203 87 9.16 665 88 10.83 335 9.99 537 39 22 9.16 289 86 9.16 753 88 10.83 247 9.99 535 38 23 9.16 374 85 9.16 841 88 10.83 159 9.99 533 37 86 85 84 24 9.16 460 86 85 9.16928 87 88 10.83 072 9.99 532 36 2 17.2 17.0 16.8 25 9.16 545 9.17016 10.82 984 9.99 530 35 3 25.8 25.5 25.2 2G 9.16631 86 9.17 103 87 10.82 897 9.99 528 34 4 34.4 34.0 33.6 27 9.16716 85 Q C 9.17 190 87 10.82 810 9.99 526 33 6 43.0 42.5 42.0 28 9.16 801 oo 9.17 277 87 10.82 723 9.99 524 32 6 51.6 51.0 50.4 29 9.16 886 85 84 9.17 363 86 87 10.82 637 9.99 522 31 7 60.2 59.5 58.8 30 9.16 970 9.17 450 10.82 550 9.99 520 30 8 68.8 68.0 67.2 31 9.17 055 85 9.17 636 86 10.82 464 9.99 518 29 9 77.4 76.5 75.6 32 *9.17 139 84 9.17 622 86 10.82 378 9.99 517 28 33 9.17 223 84 9.17 708 86 10.82 292 9.99515 27 34 9.17 307 84 9.17 794 86 10.82 206 9.99 513 26 83 82 81 35 9.17 391 84 9.17 880 86 10.82 120 9.99 511 25 2 16.6 16.4 16.2 36 9.17 474 83 9.17965 85 10.82 035 9.99 509 24 3 24.9 24.6 24.3 37 9.17 558 84 9.18051 86 10.81 949 9.99 507 23 4 33.2 32.8 32.4 38 9.17 641 83 9.18 136 85 10.81 864 9.99 505 22 5 41.5 41.0 40.5 39 9.17 724 83 9.18221 85 10.81 779 9.99 503 21 6 49.8 49.2 48.6 40 41 42 9.17 807 9.17 890 9.17 973 83 83 83 9.18 306 9.18 391 9.18 475 85 85 84 10.81 694 10.81 609 10.81 625 9.99 501 9.99 499 9.99 497 20 19 18 7 8 9 58.1 66.4 74.7 57.4 65.6 73.8 56.7 64.8 72.9 43 9.18055 82 9.18 560 85 10.81 440 9.99 495 17 44 45 9.18 137 9.18 220 82 83 9.18 644 9.18 728 84 84 10.81 356 10.81 272 9.99 494 9.99 492 16 15 From the top: 46 9.18 302 82 9.18812 84 10.81 188 9.99 490 14 For 8+ or 188+ 47 48 49 9.18 383 9.18 465 9.18 547 81 82 82 9.18 896 9.18 979 9.19 063 84 83 84 10.81 104 10.81 021 10.80 937 9.99 488 9.99 486 9.99 484 13 12 11 read as printed; for 98+ or 278+, read 50 9.18 628 81 9.19 146 83 10.80 854 9.99 482 10 co-function. 51 9.18 709 81 9.19 229 83 10.80771 9.99 480 9 52 53 9.18 790 9.18871 81 81 9.19312 9.19 395 83 83 10.80 688 10.80 605 9.99 478 9.99 476 8 7 From the bottom: 54 9.18 952 81 81 9.19478 83 83 10.80 522 9.99 474 6 For 81 0+ or 261+, 55 56 57 9.19 033 9.19 113 9.19 193 80 80 9.19 561 9.19 643 9.19 725 82 82 10.80 439 10.80 357 10.80 275 9.99 472 9.99 470 9.99 468 5 4 3 read as printed; for 171+ or 351+, read 58 9.19 273 80 9.19 807 82 10.80 193 9.99 466 2 co-function. 59 9.19 353 80 9.19 889 82 10.80111 9.99 464 1 60 9.19 433 80 9.19 971 82 10.80 029 9.99 462 LCos d LCtn cd LTan LSin / Prop. Pts. 81 Logarithms of Trigonometric Functions Ill] 9 Logarithms of Trigonometric Functions 55 ' LSin d LTan cd L Ctn L Cos Prop. Pts. 9.19433 9.19 971 10.80 029 9.99 462 60 1 9.19513 80 9.20 053 82 10.79 947 9.99 460 59 2 9.19 592 79 9.20 134 81 10.79 866 9.99 458 58 82 81 80 3 9.19 672 80 9.20216 82 10.79 784 9.99 456 57 2 16.4 16.2 16.0 4 9.19751 79 9.20 297 81 10.79 703 9.99 454 56 3 5 9.19 830 79 9.20 378 81 10.79 622 9.99 452 55 4 32.8 32i4 32!o 6 9.19 909 79 9.20 459 81 10.79 541 9.99 450 54 5 41.0 40.5 40.0 7 9.19 988 79 9.20 540 81 10.79 460 9.99 448 53 6 49.2 48.6 48.0 8 9.20 067 79 9.20621 81 10.79 379 9.99 446 52 7 57.4 56.7 56.0 9 9.20 145 78 9.20701 80 10.79 299 9.99 444 51 8 65.6 64.8 64.0 10 9.20 223 78 9.20 782 81 10.79 218 9.99 442 50 9 73.8 72.9 72.0 11 9.20 302 79 9.20 862 80 10.79 138 9.99 440 49 12 9.20 380 78 9.20 942 80 10.79 058 9.99 438 48 13 9.20 458 78 9.21 022 80 10.78 978 9.99 436 47 < 70 It 14 9.20 535 77 9.21 102 80 10.78 898 9.99 434 46 2 15.8 15.6 15.4 15 9.20 613 78 9.21 182 80 10.78 818 9.99 432 45 3 23.7 23.4 23.1 16 9.20 691 78 9.21 261 79 10.78 739 9.99 429 44 4 31.6 31.2 30.8 17 9.20 768 77 9.21 341 80 10.78 659 9.99 427 43 5 39.5 39.0 38.5 18 9.20 845 77 9.21 420 79 10.78 580 9.99 425 42 6 47.4 46.8 46.2 19 9.20 922 77 9.21 499 79 10.78 501 9.99 423 41 7 55.3 54.6 53.9 20 21 9.20 999 9.21 076 77 77 9.21 578 9.21 657 79 79 10.78 422 10.78 343 9.99 421 9.99 419 40 39 8 9 63.2 71.1 62.4 70.2 61.6 69.3 22 9.21 153 77 9.21 736 79 10.78 264 9.99 417 38 23 9.21 229 76 9.21 814 78 10.78 186 9.99 415 37 76 75 74 24 9.21 306 77 76 9.21 893 79 78 10.78 107 9.99 413 36 2 15.2 15.0 14.8 25 9.21 382 9.21 971 10.78 029 9.99411 35 3 22.8 22.5 22.2 26 9.21 458 76 9.22 049 78 10.77 951 9.99 409 34 4 30.4 30.0 29.6 27 9.21 534 76 9.22 127 78 10.77 873 9.99 407 33 5 38.0 37.5 37.0 28 9.21 610 76 9.22 205 78 10.77 795 9.99 404 32 6 45 6 45.0 44.4 29 9.21 685 75 76 9.22 283 78 78 10.77 717 9.99 402 31 7 53.2 52.5 51.8 30 9.21 761 9.22 361 10.77 639 9.99 400 30 8 60.8 60.0 59.2 31 9.21 836 75 9.22 438 77 10.77 562 9.99 398 29 9 68.4 67.5 66.6 32 9.21 912 76 9.22 516 78 10.77 484 9.99 396 28 33 9.21 987 75 9.22 593 77 10.77 407 9.99 394 27 34 9.22 062 75 9.22 670 77 10.77 330 9.99 392 26 73 72 71 35 9.22 137 75 9.22 747 77 10.77 253 9.99 390 25 2 14.6 14.4 14.2 36 9.22211 74 9.22 824 77 10.77 176 9.99 388 24 3 21.9 21.6 21.3 37 9.22 286 75 9.22 901 77 10.77 099 9.99 385 23 4 29.2 28.8 28.4 38 9.22 361 75 9.22 977 76 10.77 023 9.99 383 22 5 36.5 36.0 35.5 39 9.22 435 74 9.23 054 77 10.76 946 9.99 381 21 6 43.8 43.2 42.6 40 9.22 509 74 9.23 130 76 10.76 870 9.99 379 20 7 51.1 50.4 49.7 41 9.22 583 74 9.23 206 76 10.76 794 9.99 377 19 8 58.4 57.6 56.8 42 9.22 657 74 9.23 283 77 10.76717 9.99 375 18 9 65.7 64.8 63.9 43 9.22 731 74 9.23 359 76 10.76 641 9.99 372 17 44 9.22 805 74 9.23 435 76 10.76 565 9.99 370 16 45 9.22 878 73 9.23 510 75 10.76 490 9.99 368 15 From the top: 46 9.22 952 74 9.23 586 76 10.76414 9.99 366 14 For 9+, or 189+ 47 48 49 9.23 025 9.23 098 9.23 171 73 73 9.23 661 9.23 737 9.23 812 75 76 75 10.76 339 10.76 263 10.76 188 9.99 364 9.99 362 9.99 359 13 12 11 read as printed; for 99+ or 279+ read 50 9.23 244 73 9.23 887 75 10.76 113 9.99 357 10 co-function, 51 9.23 317 73 9.23 962 75 10.76 038 9.99 355 9 52 9.23 390 73 9.24 037 75 10.75 963 9.99 353 8 53 9.23 462 72 9.24 112 75 10.75 888 9.99 351 7 From the bottom: 54 9.23 535 73 72 9.24 186 74 10.75 814 9.99 348 6 For 80+ or 260+, 55 56 57 9.23 607 9.23 679 9.23 752 72 73 9.24 261 9.24 335 9.24 410 74 75 10.75 739 10.75 665 10.75 590 9.99 346 9.99 344 9.99 342 5 4 3 read as printed; for 170+ or 350+, read 58 9.23 823 71 9.24 484 74 10.75 516 9.99 340 2 co-function. 59 9.23 895 72 9.24 558 74 10.75 442 9.99 337 1 60 9.23 967 '- 9.24 632 74 10.75 368 9.99 335 LCos d L On cd L Tan LSin ' Prop. Pts. 80 Logarithms of Trigonometric Functions 10 Logarithms of Trigonometric Functions [III / LSin d LTan cd L Ctn L Cos d Prop. Pts. 9.23 967 9.24 632 10.75 368 9.99 335 60 1 9.24 039 72 9.24 706 74 10.75 294 9.99333 2 59 2 9.24 110 71 9.24 779 73 10.75221 9.99331 2 58 74 73 72 3 4 9.24 181 9.24 253 71 72 71 9.24 853 9.24 926 74 73 74 10.75 147 10.75 074 9.99 328 9.99 326 3 2 2 57 56 2 3 14.8 22.2 14.6 21.9 14.4 21.6 5 9.24 324 9.25 000 10.75 000 9.99 324 55 4 29.6 29.2 28.8 6 9.24 395 71 9.25 073 73 10.74 927 9.99 322 2 54 5 37.0 36.5 36.0 7 9.24 466 9.25 146 73 10.74 854 9.99319 3 53 (i 44.4 43.8 43.2 8 9.24 536 70 9.25 219 73 10.74781 9.99317 2 52 7 51.8 51.1 50.4 9 9.24 607 71 70 9.25 292 73 73 10.74708 9.99315 2 2 51 8 59.2 58.4 57.6 10 9.24 677 9.25 365 10.74 635 9.99313 50 9 66.6 65.7 64.8 11 9.24 748 71 9.25 437 72 10.74563 9.99310 3 49 12 9.24 818 70 9.25 510 73 10.74490 9.99308 2 48 13 9.24 888 70 9.25 582 72 10.74418 9.99306 2 47 71 TO 69 14 9.24 958 70 9.25 655 73 10.74 345 9.99304 2 46 2 14.2 14.0 13.8 15 9.25 028 70 9.25 727 72 10.74273 9.99301 3 45 3 21.3 21.0 20.7 16 9.25 098 70 9.25 799 72 10.74201 9.99299 2 44 4 28.4 28.0 27.6 17 9.25 168 70 9.25 871 72 10.74 129 9.99297 2 43 35.5 35.0 34.5 18 9.25237 69 9.25 943 72 10.74057 9.99 294 3 42 G 42.6 42.0 41.4 19 9.25 307 70 9.26 015 72 10.73 985 9.99 292 2 41 7 49.7 49.0 48.3 69 71 2 g 56 8 56.0 55.2 20 21 9.25 376 9.25 445 69 9.26 086 9.26 158 72 10.73 914 10.73 842 9.99 290 9.99 288 2 40 39 9 63'.9 esio 62!l 22 9.25 514 69 9.26 229 71 10.73771 9.99 285 3 38 23 9.25 583 69 9.26301 72 10.73 699 9.99283 2 37 68 67 66 24 9.25 652 69 9.26 372 71 10.73 628 9.99281 2 36 69 71 3 2 13.6 13.4 13.2 25 9.25 721 9.26 443 10.73 557 9.99 278 35 3 20.4 20.1 19.8 26 9.25 790 69 fro 9.26 514 71 10.73486 9.99270 2 34 4 27.2 26.8 26.4 27 9.25 858 OO AO 9.26 585 10.73415 9.99 274 2 33 5 34.0 33.5 33.0 28 9.25 927 Da SQ 9.26 655 70 10.73345 9.99271 32 6 40.8 40.2 39.6 29 9.25 995 DO 68 9.26 726 71 71 10.73 274 9.99 209 2 2 31 7 47.6 46.9 46.2 30 9.26 063 9.26 797 10.73 203 9.99 267 30 8 54.4 53.6 52.8 31 9.26 131 68 9.26 867 70 10.73 133 9.99264 3 29 9 61.2 60.3 59.4 32 9.26 199 68 9.26 937 70 10.73 063 9.99 262 2 28 33 9.26 267 68 9.27 008 71 10.72992 9.99 260 2 27 34 9.26 335 68 9.27 078 70 10.72 922 9.99257 3 26 65 3 2 35 9.26 403 68 o^Tjia. 70 10.72852 9.99 255 2 25 2 13.0 0.6 0.4 30 9.26470 67 T772T218 70 10.72 782 9.99252 3 24 3 19.5 0.9 0.6 37 9.26 538 68 9.27 288 70 10.72712 9.99 250 2 23 4 26.C 1.2 0.8 38 9.26 605 67 9.27 357 69 10.72643 9.99 248 2 22 5 32.5 1.5 1.0 39 9.26 672 67 9.27 427 70 10.72 573 9.99 245 3 21 6 39.C 1.8 1.2 40 9.26 739 67 9.27 496 69 10.72 504 9.99 243 2 20 7 45.5 2.1 1.4 41 9.26 806 67 9.27 566 70 10.72434 9.99241 2 19 8 52. ( 2.4 1.6 42 9.26 873 67 9.27 635 69 10.72305 9.99 238 3 18 9 58.5 2.7 1.8 43 9.26 940 67 9.27 704 69 10.72 296 9.99 236 2 17 44 9.27 007 67 9.27 773 69 10.72 227 9.99 233 3 16 45 9.27 073 66 9.27 842 69 10.72 158 9.99 231 2 15 From the top: 46 9.27 140 67 9.27911 69 10.72089 9.99 229 2 14 ForlO+orl90 0+ , 47 48 49 9.27 206 9.27 273 9.27 339 66 67 C6 9.27 980 9.28 049 9.28 117 69 69 68 10.72020 10.71951 10.71 883 9.99 226 9.99 224 9.99221 3 2 3 13 12 11 read as printed; for 100+ or 280+, read 50 9.27 405 66 9.28 186 69 10.71 814 9.99219 2 10 co-function. 51 9.27471 66 9.28 254 68 10.71746 9.99217 2 9 52 9.27537 66 9.28 323 69 10.71 677 9.99214 3 8 53 9.27 602 65 9.28391 68 10.71609 9.99212 2 7 From the bottom: 54 9.27 668 66 66 9.28 459 68 68 10.71 541 9.99209 3 2 6 For79+or259 0+ , 55 56 57 9.27 734 9.27 799 9.27 864 65 65 9.28 527 9.28 595 9.28 662 68 67 10.71 473 10.71405 10.71338 9.99 207 9.99 204 9.99202 3 2 5 4 3 read as printed; for 169+or349 0+ ,read 58 9.27 930 66 9.28 730 68 10.71 270 9.99 200 2 2 co-function. 69 9.27 995 65 9.28 798 68 10.71 202 9.99 197 3 1 60 9.28 060 65 9.28 865 67 10.71 135 9.99 195 2 L Cos d LCtn cd LTan LSin d ' Prop. Pts. 79 a Logarithms of Trigonometric Functions Ill] 11 Logarithms of Trigonometric Functions 57 / LSin d L Tan cd L Ctn L Cos d Prop. Pts. 9.28 060 9.28 865 10.71 135 9.99 195 60 1 9.28 125 65 9.28 9335 '68 10.71 067 9.99 192 3 59 2 9.28 190 55 9.29 000 67 10.71 000 9.99 190 2 58 68 67 66 3 4 9.28 254 9.28 319 64 5 65 %.29 067 9.29 134 67 67 67 10.70933 10.70866 9.99 187 9.99 185 3 2 3 57 56 2 3 13.6 20.4 13.4 20.1 13.2 19.8 5 9.28 384 9.29 201 10.70799 9.99 182 55 4 27.2 26.8 26.4 6 9.28 448 64 9.29 268 67 10.70732 9.99 180 2 54 5 34.0 33.5 33.0 7 9.28512 64 9.29 335 67 10.70 665 9.99 177 3 53 G 40.8 40.2 39.6 8 9.28 577 65 9.29 402 67 10.70598 9.99 175 - 52 7 47.6 46.9 46.2 9 9.28 641 64 9.29 468 66 10.70532 9.99 172 3 51 8 54.4 53.6 52.8 10 9.28 705 64 9.29 535 67 10.70465 9.99 170 2 50 9 61.2 60.3 59.4 11 9.28 769 64 9.29 601 66 10.70399 9.99 167 3 49 12 9.28 833 64 9.29 668 67 10.70332 9.99 165 2 48 13 9.28 896 63 9.29 734 66 10.70266 9.99 162 3 47 DO N OB 14 9.28 960 64 9.29 800 66 10.70200 9.99 160 2 46 2 13.0 12.8 12.6 15 9.29 024 64 9.29 866 66 10.70 134 9.99 157 3 45 3 19.5 19.2 18.9 16 9.29 087 63 9.29 932 66 10.70068 9.99 155 2 44 4 26.0 25.6 25.2 17 9.29 150 63 9.29 998 66 10.70002 9.99 152 3 43 5 32.5 32.0 31.5 18 9.29214 64 9.30 064 66 10.69936 9.99 150 2 42 G 39.0 38.4 37.8 19 9.29 277 63 9.30 130 66 10.69 870 9.99 147 3 41 7 45.5 44.8 44.1 20 21 9.29 340 9.29 403 63 63 9.30 195 9.30261 65 66 10.69 805 10.69739 9.99 145 9.99 142 2 3 40 39 S 9 52.0 58.5 51.2 57.6 50.4 56.7 22 9.29 466 63 9.30 326 65 10.69 674 9.99 140 2 38 23 9.29 529 63 9.30391 65 10.69 609 9.99 137 3 37 62 61 60 24 9.29 591 62 63 9.30 457 66 65 10.69 543 9.99 135 2 3 36 2 12.4 12.2 12.0 25 9.29 654 ftO 9.30 522 6" 10.69478 9.99 132 35 ,3 18.6 18.3 18.0 26 9.29 716 021 9.30 587 o 10.69413 9.99 130 2 34 4 24.8 24.4 24.0 27 9.29 779 63 9.30 652 65 - 10.69 348 9.99127 3 33 5 31.0 30.5 30.0 28 9.29 841 62 6n 9.30717 60 - 10.69283 9.99 124 3 32 6 37.2 36.6 36.0 29 9.29 903 4 63 9.30 782 o 64 10.69218 9.99 122 2 3 31 7 43.4 42.7 42.0 30 9.29 966 9.30 846 10.69 154 9.99119 30 8 49.6 48.8 48.0 31 9.30 028 62 9.30911 65 10.69089 9.99117 2 29 9 55.8 54.9 54.0 32 9.30 090 62 9.30975 64 10.69 025 9.99114 3 28 33 9.30 151 61 9.31 040 65 10.68900 9.99112 2 27 34 9.30213 62 9.31 104 64 10.68896 9.99 109 3 26 59 3 2 35 9.30 275 62 9.31 168 64 10.68 832 9.99 106 3 25 2 11.8 0.6 0.4 36 9.30 336 61 9.31 233 65 10.68767 9.99 104 2 24 3 17.7 0.9 0.6 37 9.30 398 62 9.31 297 64 10.68703 9.99 101 3 23 4 23.6 1.2 0.8 38 9.30459 61 9.31361 64 10.68 639 9.99 099 2 22 5 29.5 1.5 1.0 39 9.30 521 62 9.31 425 64 10.68575 9.99096 3 21 6 35.4 1.8 1.2 40 9.30 582 61 9.31 489 64 10.68511 9.99 093 3 20 7 41.3 2.1 1.4 41 9.30 643 61 9.31 552 63 10.68448 9.99091 2 19 S 47.2 2.4 1.6 42 9.30 704 61 9.31616 64 10.68384 9.99 088 3 18 9 53.1 2.7 1.8 43 9.30 765 61 9.31 679 63 10.68321 9.99 086 2 17 44 9.30 826 61 9.31 743 64 10.68257 9.99 083 3 16 45 9.30 887 61 9.31 806 63 10.68 194 9.99 080 3 15 From the top: 46 9.30 947 60 9.31 870 64 10.68 130 9.99078 2 14 Forll 0+ orl91+, 47 48 49 9.31 008 9.31 068 9.31 129 61 60 61 9.31 933 9.31 996 9.32 059 63 63 63 10.68067 10.68 004 10.67941 9.99075 9.99 072 9.99 070 3 3 2 13 12 11 read as printed ; for 101- | -or281 0+ ,read 50 9.31 189 60 9.32 122 63 10.67 878 9.99 067 3 10 co-function. 51 9.31 250 61 9.32 185 63 10.67815 9.99 064 3 9 52 9.31310 60 9.32 248 63 10.67752 9.99062 2 8 53 9.31 370 60 9.32 311 63 10.67 689 9.99 059 3 7 From the bottom: 54 9.31 430 60 60 9.32 373 62 63 10.67 627 9.99 056 3 2 6 For78+or258+ ? 55 56 57 9.31 490 9.31 549 9.31 609 59 60 9.32 436 9.32 498 9.32 561 62 63 10.67 564 10.67502 10.67439 9.99 054 9.99051 9.99 048 3 3 5 4 3 read as printed; for 168+ or 348+, read 58 9.31 669 60 9.32 623 62 10.67377 9.99 046 2 2 co-function. 59 9.31 728 59 60 9.32 685 62 62 10.67315 9.99 043 3 3 1 60 9.31 788 9.32 747 10.67253 9.99 040 a LCos d LCtn Cd LTan LSin d / Prop. Pts. 78 Logarithms of Trigonometric Functions 58 12 Logarithms of Trigonometric Functions [ill / LSin d LTan cd LCtn LCos d Prop. Pts. 9.31 788 9.32 747 10.67 253 9.99 040 60 1 9.31 847 59 9.32 810 63 10.67 190 9.99038 2 59 2 9.31 907 60 9.32 872 62 10.67128 9.99 035 3 58 63 62 61 3 4 9.31 966 9.32 025 59 59 59 9.32 933 9.32 995 61 62 62 10.67067 10.67 005 9.99 032 9.99 030 3 2 3 57 56 2 3 12.6 18.9 12.4 18.6 12.2 18.3 5 9.32 084 9.33 057 10.66943 9.99 027 55 4 25.2 24.8 24.4 6 9.32 143 59 9.33 119 62 10.66881 9.99 024 3 54 5 31.5 31.0 30.5 7 9.32 202 59 9.33 180 61 10.66820 9.99022 2 53 6 37.8 37.2 36.6 8 9.32 261 59 9.33 242 62 10.66758 9.99019 3 52 7 44.1 43.4 42.7 9 9.32 319 58 9.33 303 61 10.66 697 9.99016 3 51 8 50.4 49.6 48.8 10 9.32 378 59 9.33 365 62 10.66 635 9.99013 3 50 9 56.7 55.8 54.9 11 9.32 437 59 9.33 426 61 10.66 574 9.99011 2 49 12 9.32 495 58 9.33 487 61 10.66513 9.99 008 3 48 13 9.32 553 58 9.33 548 61 10.66452 9.99 005 3 47 6U 59 58 14 9.32 612 59 9.33 609 61 10.66391 9.99 002 3 46 2 12.0 11.8 11.6 15 9.32 670 58 9.33 670 61 10.66 330 9.99 000 2 45 3 18.0 17.7 17.4 16 9.32 728 58 9.33 731 61 10.66269 9.98997 3 44 4 24.0 23.6 23.2 17 9.32 786 58 9.33 792 61 10.66 208 9.98994 3 43 5 30.0 29.5 29.0 18 9.32 844 58 9.33 853 61 10.66 147 9.98991 3 42 6 36.0 35.4 34.8 19 9.32 902 58 9.33 913 60 10.66087 9.98 989 2 41 7 42.0 41.3 40.6 58 61 3 g 48.0 47.2 46.4 20 9.32 960 9.33 974 10.66 026 9.98986 40 ^3 1 21 9.33 018 58 9.34 034 60 10.65 966 9.98983 3 39 54.0 Oo.l 52.2 22 9.33 075 57 9.34 095 61 10.65905 9.98 980 3 38 23 9.33 133 58 9.34 155 60 10.65 845 9.98978 2 37 57 56 24 9.33 190 57 9.34215 60 10.65 785 9.98975 3 36 58 61 3 2 11.4 11.2 25 9.33 248 9.34 276 10.65 724 9.98 972 35 3 17.1 16.8 26 9.33 305 57 9.34 336 60 10.65664 9.98969 3 34 4 22.8 22.4 27 9.33 362 57 9.34 396 60 10.65 604 9.98967 33 5 28.5 28.0 28 9.33 420 58 9.34 456 60 10.65 544 9.98964 32 6 34.2 33 6 29 9.33 477 57 57 9.34516 60 60 10.65 484 9,98961 3 3 31 7 39.9 39.2 30 9.33 534 9.34 576 10.65 424 9.98958 30 8 45.6 44.8 31 9.33 591 57 9.34 635 59 10.65365 9.98 955 3 29 9 51.3 50.4 32 9.33 647 56 9.34 695 60 10.65305 9.98953 2 28 33 9.33 704 57 9.34 755 60 10.65 245 9.98950 3 27 34 9.33 761 57 9.34 814 59 10.65 186 9.98 947 3 26 55 3 2 35 9.33 818 57 9.34 874 60 10.65 126 9.98944 3 25 2 11.0 0.6 0.4 36 9.33 874 56 9.34 933 59 10.65067 9.98941 3 24 3 16.5 0.9 0.6 37 9.33 931 57 9.34 992 59 10.65008 9.98938 3 23 4 22.0 1.2 0.8 38 9.33 987 56 9.35051 59 10.64 949 9.98936 2 22 5 27.5 1.5 1.0 39 9.34 043 56 9.35 111 60 10.64 889 9.98933 3 21 6 33.0 1.8 1.2 40 9.34 100 57 9.35 170 59 10.64 830 9.98 930 3 20 7 38.5 2.1 1.4 41 9.34 156 56 9.35 229 59 10.64771 9.98927 3 19 8 44.C 2.4 1.6 42 9.34212 56 9.35 288 59 10.64712 9.98 924 3 18 9 49.5 2.7 1.8 43 9.34 268 56 9.35 347 59 10.64653 9.98921 3 17 44 9.34 324 56 9.35 405 58 10.64595 9.98919 2 16 45 9.34 380 56 9.35 464 59 10.64 536 9.98916 3 15 From the top: 46 9.34 436 56 9.35 523 59 10.64477 9.98913 3 14 Forl2 0+ orl92 0+ , 47 48 49 9.34491 9.34 547 9.34 602 55 56 55 9.35 581 9.35 640 9.35 698 58 59 58 10.64419 10.64360 10.64 302 9.98910 9.98907 9.98904 3 3 3 13 12 11 read as printed ; for 102 0+ or282 0+ ,read 50 9.34 658 56 9.35 757 59 10.64 243 9.98901 3 10 co-function. 51 9.34713 55 9.35 815 58 10.64 185 9.98898 3 9 52 9.34 769 56 9.35 873 58 10.64127 9.98896 2 8 53 9.34 824 55 9.35 931 58 10.64069 9.98 893 3 7 From the bottom: 54 9.34 879 55 55 9.35 989 58 58 10.64011 9.98890 3 3 6 For77- | -or257 0+ , 55 56 57 9.34 934 9.34 989 9.35 044 55 55 9.36 047 9.36 105 9.36 163 58 58 10.63 953 10.63 895 10.63 837 9.98 887 9.98 884 9.98881 3 8 5 4 3 read as printed ; for 167+ or 347+, read 58 9.35 099 55 9.36221 58 10.63779 9.98878 3 2 co-function. 59 9.35 154 55 9.36 279 58 10.63 721 9.98875 3 1 60 9.35 209 55 9.36 336 57 10.63 664 9.98 872 3 LCos d LCtn cd LTan LSin d ' Prop. Pts. 77 Logarithms of Trigonometric Functions Ill] 13 Logarithms of Trigonometric Functions 59 1 LSin d LTan cd L Ctn LCos d Prop. Pts. 9.35 209 9.36 336 10.63 664 9.98 872 60 1 9.35 263 54 9.36 394 58 10.63 606 9.98869 3 59 2 9.35 318 55 9.36 452 58 10.63 548 9.98 867 2 58 58 57 56 3 9.35 373 55 9.36 509 57 10.63491 9.98 864 3 57 2 11.6 11.4 11.2 4 9.35 427 54 54 9.36 566 57 58 10.63434 9.98861 3 56 3 16.8 5 9.35 481 9.36 624 10.63 376 9.98858 55 4 23.2 22'.8 22.4 6 9.35 536 55 9.36 681 57 10.63319 9.98 855 3 54 5 29.0 28.5 28.0 7 9.35 590 54 9.36 738 57 10.63 262 9.98 852 3 53 6 34.8 34.2 33.6 8 9.35 644 54 9.36 795 57 10.63 205 9.98849 3 52 7 10.6 39.9 39.2 9 9.35 698 54 9.36852 57 10.63 148 9.98 846 3 51 8 16.4 45.6 44.8 10 9.35 752 54 9.36 909 57 10.63091 9.98 843 3 50 9 52.2 51.3 50.4 11 9.35 806 54 9.36 966 57 10.63 034 9.98840 3 49 12 9.35 860 54 9.37 023 57 10.62977 9.98 837 3 48 9.35914 54 9.37 080 57 10.62 920 9.98 834 3 47 55 N BO 14 9.35 968 54 9.37 137 57 10.62863 9.98831 3 46 2 11.0 10.8 10.6 15 9.36 022 54 9.37 193 56 10.62 807 9.98828 3 45 3 16.5 16.2 15.9 16 9.36 075 53 9.37 250 57 10.62750 9.98825 3 44 4 22.0 21.6 21.2 17 9.36 129 54 9.37 306 56 10.62694 9.98822 3 43 5 27.5 27.0 26.5 18 9.36 182 53 9.37 363 57 10.62 637 9.98819 3 42 6 33.0 32.4 31.8 19 9.36 236 54 9.37419 56 10.62581 9.98816 3 41 7 38.5 37.8 37.1 53 57 3 8 44.0 43.2 42.4 20 9.36 289 9.37 476 10.62524 9.98 813 40 9 48.6 47.7 21 9.36 342 53 9.37 532 56 10.62468 9.98810 39 22 9.36 395 53 9.37 588 56 10.62412 9.98807 3 38 23 9.36 449 54 9.37 644 56 10.62 356 9.98 804 3 37 52 51 24 9.36 502 53 9.37 700 56 10.62300 9.98 801 3 36 53 56 3 i 10.4 10.2 25 9.36 555 9.37 756 10.62 244 9.98798 35 3 15.6 15.3 26 9.36 608 53 9.37812 56 10.62 188 9.98795 34 4 20.8 20.4 27 9.36 660 52 9.37 868 56 10.62 132 9.98792 33 5 26.0 25.5 28 9.36713 53 9.37 924 56 10.62 076 9.98789 32 6 31.2 30.6 29 9.36 766 53 53 9.37 9SO 56 55 10.62 020 9.98786 3 31 7 36.4 35.7 30 9.36 819 9.38 035 10.61 965 9.98783 30 8 41.6 40.8 31 9.36 871 52 9.38091 56 10.61909 9.98780 3 29 9 46.8 45.9 32 9.36 924 53 9.38 147 56 10.61853 9.98777 3 28 33 9.36 976 52 9.38 202 55 10.61798 9.98774 3 27 34 9.37 028 52 9.38 257 55 10.61 743 9.98771 3 26 4 3 2 35 9.37 081 53 9.38313 56 10.61 687 9.98768 3 25 2 0.8 0.6 0.4 36 9.37 133 52 9.38 368 55 10.61 632 9.98765 3 24 3 1.2 0.9 0.6 37 9.37 185 52 9.38423 55 10.61577 9.98762 3 23 4 1.6 1.2 0.8 38 9.37 237 52 9.38 479 56 10.61521 9.98759 3 22 5 2.0 1.5 1.0 39 9.37 289 52 9.38 534 55 10.61 466 9.98756 3 21 6 2.4 1.8 1.2 40 9.37 341 52 9.38 589 55 10.61411 9.98 753 3 20 7 2.8 2.1 1.4 41 9.37 393 52 9.38 644 55 10.61356 9.98750 3 19 8 3.2 2.4 1.6 42 9.37 445 52 9.38 699 55 10.61301 9.98746 4 18 9 3.6 2.7 1.8 43 9.37 497 52 9.38 754 55 10.61 246 9.98743 3 17 44 9.37 549 52 9.38 808 54 10.61 192 9.98740 3 16 45 9.37 600. 51 9.38 863 55 10.61 137 9.98737 3 15 From the top: 46 9.37 652 52 9.38918 55 10.61082. 9.98734 3 14 F or 13 0+ or 193 0+ 47 48 49 9.37 703 9.37 755 9.37 806 51 52 51 9.38972 9.39 027 9.39 082 54 55. 55 10.61 028 10.60973 10.60918 9.98731 9.98728 9.98725 3 3 13 12 11 read as printed; for 103 0+ or283 0+ ,read 50 9.37 858 52 9.39 136 54 10.60 864 9.98722 3 10 co-function. 51 9.37 909 51 9.39 190 54 10.60810 9.98719 3 9 52 9.37 960 51 9.39 245 55 10.60755 9.98715 4 8 53 9.38011 51 9.39 299 54 10.60701 9.98712 3 7 From the bottom: 54 9.38 062 51 51 9.39 353 54 54 10.60647 9.98709 3 3 6 For 76+ or 256+, 55 56 57 9.38 113 9.38 164 9.38215 51 51 9.39 407 9.39 461 9.39 515 54 54 10.60593 10.60539 10.60485 9.98706 9.98 703 9.98700 3 3 5 4 3 read as printed ; for 166+ or 346+ read 58 9.38 266 51 9.39 569 54 10.60431 9.98697 3 2 co-function. 59 9.38317 51 9.39 623 54 10.60377 9.98694 3 1 60 9.38 368 51 9.39 677 54 10.60323 9.98 690 4 LCos d LCtn cd L Tan LSin "d ' Prop. Pts. 76 Logarithms of Trigonometric Functions 60 14 Logarithms of Trigonometric Functions [III ' LSin d LTan cd L Ctn L Cos d Prop. Pts. 9.38 368 9.39 677 10.60323 9.98 690 60 1 9.38 418 50 9.39731 54 10.60269 9.98687 3 59 2 9.38 469 51 9.39 785 54 10.60215 9.98684 3 58 54 53 52 3 4 9.38519 9.38 570 50 51 50 9.39 838 9.39 892 53 54 53 10.60 162 10.60 108 9.98681 9.98678 3 3 3 57 56 2 3 10.8 16.2 10.6 15.9 10.4 15.6 5 9.38 620 9.39 945 10.60055 9.98 675 55 4 21 6 21 .2 20.8 6 9.38 670 50 9.39 999 54 10.60001 9.98671 4 54 5 27.0 26.5 26.0 7 9.38 721 51 9.40 052 53 10.59 948 9.98 668 3 53 6 32.4 31 .8 31.2 8 9.38771 50 9.40 106 54 10.59894 9.98665 3 52 7 37.8 37.1 36.4 9 9.38 821 50 9.40 159 53 10.59 841 9.98 662 3 51 8 43 2 42.4 41.6 10 9.38 871 50 9.40 212 53 10.59 788 9.98659 3 50 9 48.6 47.7 46.8 11 9.38 921 50 9.40 266 54 10.59734 9.98 656 3 49 12 9.38 971 50 9.40 319 1 53 10.59681 9.98652 4 48 13 9.39 021 50 9.40 372 53 10.59 628 9.98649 3 47 51 50 49 14 9.39 071 50 9.40 425 53 10.59 575 9.98 646 3 2 10.2 10.0 9.8 15 9.39 121 50 9.40 478 53 10.59 522 9."98l54T 3 45 3 15 3 15.0 14.7 16 9.39 170 49 9.40 531 53 10.59469 9.98640 3 44 4 204 20.0 19.6 17 9.39 220 50 9.40 684 53 10.59416 9.98636 4 43 5 25 5 25.0 24.5 18 9.39 270 50 9.40 636 52 10.59 364 9.98633 3 42 8 30 6 30.0 29.4 19 9.39 319 49 9.40 689 53 10.59311 9.98 630 3 41 7 35 7 35.0 34.3 20 21 9.39 369 9.39418 50 49 9.40 742 9.40 795 53 53 10.59 258 10.59 205 9.98627 9.98623 3 4 40 39 8 9 40.8 45.9 40.0 45.0 39.2 44.1 22 9.39 467 49 9.40 847 52 10.59 153 9.98620 3 38 23 9.39 517 50 9.40 900 53 10.59 100 9.98617 3 37 4& 47 24 9.39 566 49 9.40 952 52 53 10.59 048 9.98614 3 4 36 2 fi 9.4 25 9.39 615 9.41 005 10.58 995 9.98 610 35 3 14.4 14.1 26 9.39 604 49 9.41 057 52 10.58943 9.98607 34 4 19.2 18.8 27 9.39713 49 9.41 109 52 10.58891 9.98604 3 33 5 24.0 23.5 28 9.39 762 49 9.41 161 52 10.58839 9.98601 3 32 6 28.8 28.2 29 9.39811 49 49 9.41 214 53 52 il0.58786 9.98597 4 3 31 7 33.6 32.9 30 9.39 860 9.41 266 10.58734 9.98594 30 8 38.4 37.6 31 9.39 909 49 9.41318 52 10.58682 9.98591 3 29 9 43.2 42.3 32 9.39 958 49 9.41 370 52 10.58630 9.98588. 3 28 33 9.40 006 48 9.41 422 52 10.58578 9.98584' 4 27 34 9.40 055 49 9.41 474 52 10.58526 9.98581 3 26 4 3 35 9.40 103 48 9.41 626 52 10.58474 9.98578 3 25 2 0.8 0.6 36 9.40 152 49 9.41 678 52 10.58422 9.98574 4 24 3 1.2 0.9 37 9.40 200 48 9.41 629 51 10.58371 9.98571 3 23 4 1 .6 1.2 38 9.40 249 49 9.41 681 52 10.58319 9.98568 3 22 5 2.0 1.5 39 9.40 297 48 9.41 733 52 10.58267 9.98665 3 21 6 2.4 1. S 40 9.40 346 49 9.41 784 51 10.58216 9.98561 4 20 7 2.8 2.1 41 9.40 394 48 9.41 836 52 10.58 164 9.98558 3 19 8 3.2 2.4 42 9.40 442 48 9.41 887 51 10.58113 9.98555 3 18 9 3.6 2.7 43 9.40 490 48 9.41 939 52 10.58061 9.98551 4 17 44 9.40 638 48 9.41990 51 10.58010 9.98548 3 16 45 9.40 686 48 9.42 041 51 10.57959 9.98545 3 15 From the top: 46 9.40 634 48 9.42 093 52 10.57 907 9.98541 4 14 Forl4 0+ orl94 0+ , 47 48 49 9.40 682 9.40 730 9.40 778 48 48 48 9.42 144 9.42 195 9.42 246 51 51 51 10.57856 10.57805 10.57 754 9.98538 9.98535 9.98531 3 4 13 12 11 read as printed; for 104- | -or284+,read 50 9.40 825 47 9.42 297 51 10.57 703 9.98 528 3 10 co-function. 51 9.40 873 48 9.42 348 51 10.57 652 9.98 525 3 9 52 53 9.40 921 9.40 968 48 47 9.42 399 9.42 450 51 51 10.57601 10.57550 9.98521 9.98518 4 3 8 7 From the bottom: 54 9.41 016 48 47 9.42 501 51 51 10.57499 9.98515 3 4 6 For75 0+ or255 0+ , 55 56 57 9.41 063 9.41 111 9.41 158 48 47 9.42 552 9.42 603 9.42 653 51 50 10.57448 10.57397 10.57 347 9.98511 9.98508 9.98505 3 8 5 4 3 read as printed; for 165^or345 0+ ,read 58 9.41 205 47 9.42 704 51 10.57 296 9.98501 4 2 co-function. 59 9.41 252 47 9.42 755 51 10.57 245 9.98498 3 1 60 9.41 300 48 9.42 805 50 10.57 195 9.98 494 4 LCos d LCtn cd LTan LSin d ' Prop. Pts. 75 Logarithms of Trigonometric Functions Ill] 15 Logarithms of Trigonometric Functions 61 / LSin d LTan cd LCtn LCos d Prop. Pts. 9.41 300 9.42 805 10.57 195 9.98494 60 1 9.41 347 47 9.42 856 51 10.57 144 9.98491 3 59 2 9.41 394 47 9.42 906 50 10.57094 9.98488 3 58 51 50 49 3 4 9.41 441 9.41 488 47 47 47 9.42 957 9.43 007 51 50 50 10.57 043 10.56993 9.98484 9.98481 4 3 4 57 56 2 3 10.S 15.: ! 10.0 ! 15.0 9.8 14.7 5 9.41 535 9.43 057 10.56 943 9.98477 55 4 20.^ I 20.0 19.6 6 9.41 582 47 9.43 108 51 10.56 892 9.98474 3 54 5 25.1 > 25.0 24.5 7 9.41 628 46 9.43 158 50 10.56842 9.98471 3 53 G 30.( > 30.0 29.4 8 9.41 675 47 9.43 208 50 10.56792 9.98467 4 52 7 35.1 ' 35.0 34.3 9 9.41 722 47 dfi 9.43 258 50 50 10.56 742 9.98464 3 .^ 51 S 40.* \ 40.0 39.2 10 9.41 768 ^u 9.43 308 10.56 692 9.98460 50 9 45.J 1 45.0 44.1 11 9.41 815 47 9.43 358 50 10.56 642 9.98457 3 49 12 9.41 861 46 9.43 408 50 10.56592 9.98453 4 48 13 9.41 908 47 9.43 458 50 10.56542 9.98450 3 47 48 4f 46 14 9.41 954 46 9.43 508 50 10.56492 9.98 *47 3 46 2 9.6 . 9.4 9.2 15 9.42 001 47 9.43 558 50 10.56442 9.98443 4 45 3 14.4 t 14.1 13.8 16 9.42 047 46 9.43 607 49 10.56393 9.98440 3 44 4 19.S , 18.8 18.4 17 9.42 093 46 9.43 657 50 10.56343 9.98436 4 43 5 24.C 1 23.5 23.0 18 9.42 140 47 9.43 707 50 10.56293 9.98433 3 42 G 28.8 \ 28.2 27.6 19 9.42 186 46 9.43 756 49 10.56 244 9.98429 4 41 7 33.6 32.9 32.2 20 21 9.42 232 9.42 278 46 46 9.43 806 9.43 855 50 49 10.56 194 10.56 145 9.98426 9.98422 3 4 40 39 S 9 38.4 43.2 : 37.6 42.3 36.8 41.4 22 9.42 324 46 9.43 905 50 10.56095 9.98419 3 38 23 9.42 370 46 46 9.43 954 49 50 10.56046 9.98415 4 37 45 44 24 9.42 416 9.44 004 10.55 996 9.98412 o 36 45 49 3 2 9.0 j .8 25 9.42 461 9.44 053 10.55 947 9.98409 35 3 ] 3.5 13 9 26 9.42 507 46 9.44 102 49 10.55 898 9.98405 4 34 4 ] 8.0 17^6 27 9.42 553 46 9.44 151 49 10.55 849 9.98402 3 33 5 2 2.5 22.0 28 9.42 599 46 9.44 201 50 10.55799 9.98398 4 32 6 2 7.0 26.4 29 9.42 644 45 46 9.44 250 49 49 10.55 750 9.98395 3 4 31 7 3 1.5 3o!s 30 9.42 690 9.44 299 10.55 701 9.98391 30 8 3 6.0 35.2 31 9.42 735 45 9.44 348 49 10.55 652 9.98 3SS 3 .29- 9 4 0.5 39.6 32 9.42 781 46 9.44 397 49 10.55 603 9.98384 4 28 33 9.42 826 45 9.44 446 49 10.55 554 9.98381 3 27 34 9.42 872 46 45 9.44 495 49 49 10.55505 9.98 377 4 4 26 4 3 35 9.42 917 9.44 544 10.55 456 9.98373 25 2 0.8 0.6 36 9.42 962 45 9.44 592 48 10.55408 9.98370 3 24 3 1.2 0.9 37 9.43 008 46 9.44 641 49 10.55359 9.98366 4 2o 4 1.6 1.2 38 9.43 053 45 9.44 690 49 10.55310 9.98363 3 22 5 2.0 1.5 39 9.43 098 45 9.44 738 48 10.55 262 9.98359 4 21 6 2.4 14 J 40 9.43 143 45 9.44 787 49 10.55213 9.98356 3 20 7 2.8 2.1 41 9.43 188 45 9.44 836 49 10.55 164 9.98352 4 19 8 3.2 2.4 42 9.43 233 45 9.44 884 48 10.55116 9.98349 3 18 9 3.6 2.7 43 9.43 278 45 9.44 933 49 10.55 067 9.98345 4 17 44 9.43 323 45 9.44 981 48 10.55019 9.98342 3 16 45 9.43 367 44 9.45 029 48 10.54971 9.98338 4 15 From the top: 46 9.43 412 45 9.45 078 49 10.54922 9.98334 4 14 Forl5->-orl95 +, 47 48 49 9.43 457 9.43 502 9.43 546 45 45 44 9.45 126 9.45 174 9.45 222 48 48 48 10.54874 10.54 826 10.54778 9.98331 9.98327 9.98324 3 4 3 13 12 11 read as printed ; for 105 0+ or285 0+ ,read 50 9.43 591 45 9.45 271 49 10.54 729 9.98320 4 10 co-function. 51 9.43 635 44 9.45 319 48 10.54 681 9.98317 3 9 52 9.43 680 45 9.45 367 48 10.54633 9.98313 4 8 53 9.43 724 44 9.45415 48 10.54 585 9.98309 4 7 From the bottom: 54 9.43 769 45 44 9.45 463 48 48 10.54 537 9.98306 3 4 6 For 74+ or 254+, 55 56 57 9.43 813 9.43 857 9.43 901 44 44 9.45511 9.45 559 9.45 606 48 47 10.54 489 10.54441 10.54394 9.98302 9.98299 9.98295 3 4 5 4 3 read as printed; for 164+ or 344+, read 58 9.43 946 45 9.45 654 48 10.54 346 9.98291 4 2 co-function. 59 9.43 990 44 44 9.45 702 48 48 10.54 298 9.98288 3 4 1 60 9.44 034 9.45 750 10.54 250 9.98 284 LCos d L Ctn cd LTan LSin d / Prop. Pts. 74 Logarithms of Trigonometric Functions 62 16 Logarithms of Trigonometric Functions [III 1 LSin d LTan cd LCtn L Cos d Prop. Pts. 9.44 034 9.45 750 10.54 250 9.98 284 60 1 9.44 078 44 9.45 797 47 10.54203 9.98281 3 59 2 9.44 122 44 9.45 845 48 10.54 155 9.98 277 4 58 48 47 46 3 9.44 166 44 9.45 892 47 10.54 108 9.98273 4 57 2 9.6 9.4 9 2 4 9.44 210 44 43 9.45 940 48 47 10.54 060 9.98 270 3 4 56 3 13^8 5 9.44 253 9.45 987 10.54013 9.98 266 55 4 19.2 18.8 18.4 6 9.44 297 44 9.46 035 48 10.53 965 9.98262 4 54 5 24.C 23.5 23.0 7 9.44 341 44 9.46 082 47 10.53918 9.98259 3 53 6 28.S 28.2 27.6 8 9.44 385 44 9.46 130 48 10.53 870 9.98255 4 52 7 33.e 32.9 32.2 9 9.44 428 43 9.46 177 47 10.53 823 9.98251 4 51 8 38.4 37.6 36.8 10 9.44 472 44 9.46 224 47 10.53 776 9.98 248 3 50 9 43.2 42.3 41.4 11 9.44 516 44 9.46 271 47 10.53 729 9.98 244 4 49 12 9.44 559 43 9.46 319 48 10.53 681 9.98240 4 48 13 9.44 602 43 9.46 366 47 10.53 634 9.98237 3 47 45 44 43 14 9.44 646 44 9.46413 47 10.53 587 9.98 233 4 46 2 9.C 8.8 8.6 15 9.44 689 43 9.46 460 47 10.53 540 9.98 229 4 45 3 13.S 13.2 12.9 16 9.44 733 44 9.46 507 47 10.53 493 9.98226 3 44 4 18. C 17.6 17.2 17 9.44 776 43 9.46 554 47 10.53 446 9.98222 4 43 5 22. 22.0 21.5 18 9.44 819 43 9.46 601 47 10.53399 9.98218 4 42 6 27.C 26.4 25.8 19 9.44 862 43 9.46 648 47 10.53352 9.98215 3 41 7 31. 30.8 30.1 43 46 4 g 36. C 35 i 34.4 20 9.44 905 9.46 694 10.53 306 9.98211 40 40 c QO ^ OQ T 21 9.44 948 43 9.46741 47 10.53 259 9.98207 4 39 OB OS. / 22 9.44 992 44 9.46 788 47 10.53212 9.98 204 3 38 23 9.45 035 43 9.46 835 47 10.53 165 9.98200 4 37 40 41 24 9.45 077 42 43 9.46 881 46 47 10.53119 9.98 196 4 4 36 2 VM 8.4 25 9.45 120 9.46 928 10.53 072 9.98 192 35 3 1 2.6 12.3 26 9.45 163 43 9.46 975 47 10.53 025 9.98189 34 4 ] 6.8 16.4 27 9.45 206 43 9.47 021 46 10.52979 9.98 185 4 33 5 2 1.0 20.5 28 9.45 249 43 9.47 068 47 10.52932 9.98181 32 6 2 5.2 24.6 29 9.45 292 43 42 9.47 114 46 46 10.52 886 9.98177 4 3 31 7 2 9.4 28.7 30 9.45 334 9.47 160 10.52 840 9.98 174 30 8 3 3.6 32.8 31 9.45 377 43 9.47 207 47 10.52793 9.98170 4 29 9 5 7.8 36.9 32 9.45419 42 9.47 253 46 10.52747 9.98166 4 28 33 9.45 462 43 9.47 299 46 10.52701 9.98162 4 27 34 9.45 504 42 9.47 346 47 10.52654 9.98 159 3 26 4 3 35 9.45 547 43 9.47 392 46 10.52 608 9.98 155 4 25 2 0.8 0.6 36 9.45 589 42 9.47 438 46 10.52562 9.98 151 4 24 3 1.2 0.9 37 9.45 632 43 9.47 484 46 10.52516 9.98 147 4 23 4 1.6 1.2 38 9.45 674 42 9.47 530 46 10.52470 9.98 144 3 22 5 2.0 1.5 39 9.45 716 42 9.47 576 46 10.52424 9.98 140 4 21 6 2.4 1.8 40 9.45 758 42 9.47 622 46 10.52 378 9.98 136 4 20 7 2.8 2.1 41 9.45 801 43 9.47 668 46 10.52332 9.98 132 4 19 8 3.2 2.4 42 9.45 843 42 9.47 714 46 10.52286 9.98129 3 18 9 3.6 2.7 43 9.45 885 42 9.47 760 46 10.52240 9.98125 4 17 44 9.45 927 42 9.47 806 46 10.52 194 9.98121 4 16 45 9.45 969 42 9.47 852 46 10.52 148 9.98117 4 15 From the top: 46 9.46011 42 9.47 897 45 10.52 103 9.98113 4 14 For 16+ or 196+, 47 48 49 9.46 053 9.46 095 9.46 136 42 42 41 9.47 943 9.47 989 9.48 035 46 46 46 10.52 057 10.52011 10.51965 9.98110 9.98106 9.98 102 3 4 4 13 12 11 read as printed ; for 106+ or 286+, read 50 9.46 178 42 9.48 080 45 10.51920 9.98098 4 10 co-function. 51 9.46 220 42 9.48 126 46 10.51874 9.98094 4 9 52 9.46 262 42 9.48 171 45 10.51 829 9.98090 4 8 53 9.46 303 41 9.48 217 46 10.51 783 9.98087 3 7 From the bottom: 54 9.46 345 42 41 9.48 262 45 45 10.51738 9.98083 4 4 6 For 73+ or 253+ 55 56 57 9.46 386 9.46 428 9.46 469 42 41 9.48 307 9.48 353 9.48 398 46 45 10.51693 10.51 647 10.51 602 9.98 07& 9.98075 9.98071 4 4 5 4 3 read as printed; for 163+ or 343+, read 58 9.46511 42 9.48 443 45 10.51557 9.98067 4 2 co-function. 59 9.46 552 41 9.48 489 46 10.51511 9.98063 4 1 42 45 3 60 9.46 594 9.48 534 10.51 466 9.98060 LCos d L Ctn cd L Tan LSin d ' Prop. Pts. Logarithms of Trigonometric Functions Ill] 17 Logarithms of Trigonometric Functions 63 L Sin d L Tan cd L Ctn L Cos d Prop. Pts. 9.46 594 9.48 534 10.51466 9.98 060 60 1 9.46 635 41 9.48 579 45 10.51421 9.98 056 4 59 2 9.46 676 41 9.48 624 45 10.51 376 9.98 052 4 58 45 44 43 3 9.46 717 41 9.48 669 45 10.51331 9.98 048 4 57 n f\ ( > o c 4 9.46 758 41 42 9.48 714 45 45 10.51 286 9.98 044 4 4 56 3 y.u 13.5 13.'. > 8.6 I 12.9 5 9.46 800 9.48 759 10.51 241 9.98 040 55 4 18.0 5 17.2 6 9.46841 41 9.48 804 45 10.51 196 9.98036 4 54 5 22.5 22.( ) 21.5 7 9.46 882 41 9.48 849 45 10.51 151 9.98 032 4 53 6 27.0 26." I 25.8 8 9.46 923 41 9.48 894 45 10.51 106 9.98 029 3 52 7 31 5 30.J \ 30.1 9 9.46 964 41 41 9.48 939 45 45 10.51 061 9.98 025 4 4 51 8 36.0 35.5 J 34.4 10 9.47 005 9.48 984 10.51016 9.98021 50 9 40.5 39.( 5 38.7 11 9.47 045 40 9.49 029 45 10.50971 9.98017 4 49 12 9.47 086 41 9.49 073 44 10.50927 9.98013 4 48 13 9.47 127 41 9.49 118 45 10.50882 9.98 009 4 47 42 41 40 14 9.47 168 41 9.49 163 45 10.50837 9.98 005 4 46 2 8.4 8.; J 8.0 15 9.47 209 41 9.49 207 44 10.50 793 9.98 001 4 45 3 12.6 12.; \ 12.0 16 9.47 249 40 9.49 252 45 10.50 748 9.97 997 4 44 4 16.8 16." I 16.0 17 9.47 290 41 9.49 296 44 10.50704 9.97 993 4 43 5 21 20.i > 20.0 18 9.47 330 40 9.49 341 45 10.50659 9.97 989 4 42 6 25.2 24.( > 24.0 19 9.47 371 41 9.49 385 44 10.50615 9.97 986 3 41 7 29.4 28.' r 28.0 20 21 9.47411 9.47 452 40 41 9.49 430 9.49 474 45 44 10.50 570 10.50 526 9.97 982 9.97 978 4 4 40 39 8 9 33.6 37.8 32.* 36.< \ 32.0 ) 36.0 22 9.47 492 40 9.49 519 45 10.50481 9.97 974 4 38 23 9.47 533 41 9.49 563 44 10.50437 9.97 970 4 37 TO 24 9.47 573 40 9.49 607 44 10.50 393 9.97 966 4 36 O7 25 9.47 613 40 9.49 652 45 10.50348 9.97 962 4 35 2 7.8 ni 1.0 1 H 26 9.47 654 41 9.49 696 44 10.50304 9.97 958 4 34 4 , i 15.6 l.O 2 n 27 9.47 694 40 9.49 740 44 10.50 260 9.97 954 4 33 5 19.5 DV 2.5 28 9.47 734 40 9.49 784 44 10.50216 9.97 950 4 32 g 23.4 29 9.47 774 40 40 9.49 828 44 44 10.50172 9.97 946 4 4 31 7 3.5 30 9.47 814 9.49 872 10.50 128 9.97 942 30 8 31.2 4.0 31 9.47 854 40 9.49 916 44 10.50084 9.97 938 4 29 9 35.1 1.5 32 9.47 894 40 9.49 960 44 10.50 040 9.97934 4 28 33 9.47 934 40 9.50 004 44 10.49 996 9.97 930 4 27 34 9.47 974 40 40 9.50 048 44 44 10.49 952 9.97 926 4 4 26 4 3 35 9.48 014 9.50 092 10.49 908 9.97 922 25 2 0.8 C 1.6 36 9.48 054 40 9.50 136 44 10.49 864 9.97918 4 24 3 1 .2 C 37 9.48 094 40 9.50 180 44 10.49820 9.97914 4 23 4 1 .6 1 .2 38 9.48 133 39 9.50 223 43 10.49 777 9.97910 4 22 5 2 .0 1 .5 39 9.48 173 40 9.50 267 44 10.49 733 9.97906 4 21 6 2 .4 1 .8 40 9.48 213 40 9.50311 44 10.49689 .97 902 4 20 7 2 .8 2 .1 41 9.48 252 39 9.50 355 44 10.49 645 9.97 898 4 19 8 3 .2 2 .4 42 9.48 292 40 9.50398 43 10.49 602 9.97 894 4 18 9 3 .6 2 .7 43 9.48 332 40 9.50 442 44 10.49558 9.97 890 4 17 44 9.48 371 39 9.50 485 43 10.49515 9.97 886 4 16 45 9.48411 40 9.50 529 44 10.49471 9.97 882 4 15 From the top: 46 9.48 450 39 9.50572 43 10.49428 9.97878 4 14 For 17+ or 197+, 47 48 49 9.48 490 9.48 529 9.48 568 40 39 39 9.50 616 9.50 659 9.50 703 44 43 44 10.49 384 10.49341 10.49 297 9.97 874 9.97 870 9.97 866 4 4 4 13 12 11 read as printd; for 107+ or 287+, read 50 9.48 607 39 9.50 746 43 10.49 254 9.97 861 10 co-function. 51 9.48 647 40 9.50 789 43 10.49211 9.97 857 4 9 52 9.48 686 39 9.50 833 44 10.49 167 9.97 853 4 8 53 9.48 725 39 9.50 876 43 10.49 124 9.97 849 4 7 From the bottom: 54 9.48 764 39 39 9.50919 43 43 10.49 081 9.97845 4 4 6 For 72+ or 252+ 55 56 57 9.48 803 9.48 842 9.48 881 39 39 9.50 962 9.51 005 9.51 048 43 43 10.49 038 10.48995 10.48 952 9.97841 9.97 837 9.97 833 4 4 5 4 3 read as printed ; for 162 0+ or342- t -,read 58 9.48 920 39 9.51 092 44 10.48908 9.97 829 4 2 co-furction. 59 9.48 959 39 39 9.51 135 43 43 10.48 865 9.97 825 4 1 60 9.48 998 9.51 17S 10.48822 9.97821 LCos d L Ctn c d L Tan LSin d ' Prop. Pts. 72 Logarithms of Trigonometric Functions 64 18 Logarithms of Trigonometric Functions [III ' LSin d LTan cd L Ctn L Cos d Prop. Pts. 9.48 998 9.51 178 10.48 822 9.97821 60 1 9.49 037 39 9.51 221 43 10.48779 9.97817 4 59 2 9.49 076 39 9.51 264 43 10.48736 9.97812 5 58 3 9.49 115 39 9.51 306 42 10.48694 9.97 808 4 57 4 9.49 153 38 9.51 349 43 10.48651 9.97 804 4 56 5 9.49 192 39 9.51 392 43 10.48608 9.97 800 4 55 43 42 41 6 7 8 9 9.49 231 9.49 269 9.49 308 9.49 347 39 38 39 39 38 9.51 435 9.51 478 9.51 520 9.51 563 43 43 42 43 43 10.48565 10.48522 10.48480 10.48437 9.97 796 9.97792 9.97 788 9.97 784 4 4 4 4 5 54 53 52 51 2 3 4 5 8.6 12.9 17.2 21.5 8.4 12.6 16.8 21.0 8.2 12.3 16.4 20.5 10 9.49 385 9.51 606 10.48394 9.97 779 50 6 25.8 25.2 24.6 11 9.49 424 39 9.51 648 42 10.48352 9.97775 4 49- 7 30.1 29.4 28.7 12 9.49 462 38 9.51 691 43 10.48309 9.97771 4 48 8 34.4 33.6 32.8 13 9.49 500 38 9.51 734 43 10.48266 9.97 767 4 47 9 38.7 37.8 36.9 14 9.49 539 39 9.51 776 42 10.48224 9.97763 4 46 15 9.49 577 38 9.51 819 43 10.48 181 9.97759 4 45 16 9.49 615 38 9.51 861 42 10.48 139 9.97 754 5 44 oq 00 17 9.49 654 39 9.51 903 42 10.48097 9.97750 4 43 O*7 oo 01 18 9.49 692 38 9.51 946 43 10.48054 9.97746 4 42 2 7.8 7.6 7.4 19 9.49 730 38 9.51 988 42 10.48012 9.97742 4 41 3 11.7 11.4 11.1 20 21 22 23 24 9.49 768 9.49 806 9.49 844 9.49 882 9.49 920 38 38 38 38 38 38 9.52 031 9.52 073 9.52 115 9.52 157 9.52 200 43 42 42 42 43 42 10.47969 10.47927 10.47 885 10.47843 10.47 800 9.97738 9.97 734 9.97 729 9.97 725 9.97721 4 4 5 4 4 4 40 39 38 37 36 4 5 6 7 8 9 15.6 19.5 23.4 27.3 31.2 35.1 15.2 19.0 22.8 26.6 30.4 34.2 14.8 18.5 22.2 25.9 29.6 33.3 25 9.49 958 9.52 242 10.47758 9.97717 35 26 9.49 996 38 9.52 284 42 10.47716 9.97713 4 34 27 9.50 034 38 9.52 326 42 10.47674 9.97 708 5 33 28 9.50 072 38 9.52 368 42 10.47 632 9.97704 4 32 36 5 4 29 9.50 110 38 9.52 410 42 10.47 590 9.97700 4 31 2 7.2 1.0 0.8 30 9.50 148 38 9.52 452 42 10.47548 9.97696 4 30 3 10.8 1.5 1.2 31 9.50 185 37 9.52 494 42 10.47 506 9.97691 5 29 4 14.4 2.0 1.6 32 9.50 223 38 9.52 536 42 10.47464 9.97 687 4 28 5 18.0 2.5 2.0 33 9.50 261 38 9.52 578 42 10.47422 9.97 683 4 27 6 21.6 3.0 2.4 34 9.50 298 37 9.52 620 42 10.47 380 9.97679 4 26 7 25.2 3.5 2.8 35 36 9.50 336 9.50 374 38 38 9.52 661 9.52 703 41 42 10.47 339 10.47 297 9.97 674 9.97 670 5 4 25 24 8 9 32.4 4.0 4.5 3.2 3.6 37 9.50411 37 9.52 745 42 10.47 255 9.97666 4 23 38 9.50 449 38 9.52 787 42 10.47213 9.97662 4 22 39 9.50 486 37 9.52 829 42 10.47 171 9.97657 5 21 40 9.50 523 37 9.52 870 41 10.47 130 9.97 653 4 20 41 9.50561 38 9.52912 42 10.47 088 9.97 649 4 19 42 9.50 598 37 9.52 953 41 10.47 047 9.97 645 4 18 From the top: 43 44 9.50 635 9.50 673 37 38 9.52 995 9.53 037 42 42 10.47 005 10.46 963 9.97 640 9.97 636 5 4 17 16 For 18+ or 198+ 45 9.50710 37 9.53 078 41 10.46922 9.97632 4 15 read as printed; for 46 9.50 747 37 9.53 120 42 10.46 880 9.97628 4 14 108 0+ or288- 1 -,read 47 9.50 784 37 9.53 161 41 10.46 839 9.97 623 5 13 co-function. 48 9.50821 37 9.53 202 41 10.46798 9.97619 4 12 49 9.50 858 37 9.53 244 42 10.46 756 9.97615 4 11 50 9.50 896 38 9.53 285 41 10.46 715 9.97610 5 10 From the bottom: 51 9.50 933 37 9.53 327 42 10.46673 9.97606 4 9 For 71+ or 251+, 52 53 54 9.50 970 9.51 007 9.51 043 37 37 36 9.53 368 9.53 409 9.53 450 41 41 41 10.46632 10.46591 10.46550 9.97 602 9.97597 9.97593 4 5 4 8 7 6 read as printed; for 161+ or 341+, read 55 9.51 080 37 9.53 492 42 10.46508 9.97589 4 5 co-function. 56 9.51 117 37 9.53 533 41 10.46467 9.97584 5 4 57 9.51 154 37 9.53 574 41 10.46426 9.97580 4 3 58 9.51 191 37 9.53615 41 10.46385 9.97576 4 2 59 9.51 227 36 9.53 656 41 10.46344 9.97571 5 1 60 9.51 264 37 9.53 697 41 10.46303 9.97567 4 LCos d LCtn cd LTan LSin d 1 Prop. Pts. 71 Logarithms of Trigonometric Functions Ill] 19 Logarithms of Trigonometric Functions 65 ' LSin d L Tan cd L Ctn LCos d Prop. Pts. 9.51 264 9.53 697 10.46 303 9.97 567 60 1 9.51 301 37 9.53 738 41 10.46 262 9.97563 4 59 2 9.51 338 37 9.53 779 41 10.46 221 9.97558 5 58 3 9.51 374 36 9.53 820 41 10.46 180 9.97554 4 57 4 9.51411 37 9.53 861 41 10.46 139 9.97550 4 56 5 9.51 447 36 9.53 902 41 10.46098 9.97545 5 55 41 40 39 6 9.51 484 37 9.53 943 41 10.46 057 9.97541 4 54 2 8.2 8.0 7.8 7 9.51 520 36 3-r 9.53 984 41 10.46016 9.97536 5 53 3 12.0 1L7 8 9 9.51 557 9.51 593 7 36 36 9.54 025 9.54 065 41 40 41 10.45975 10.45 935 9.97532 9.97528 4 4 d 52 51 4 5 ie!4 20.5 16.0 20.0 15.6 19.5 10 9.51 629 9.54 106 10.45 894 9.97523 50 6 24.6 24.0 23.4 11 9.51 666 37 9.54 147 41 10.45 853 9.97519 4 49 7 28.7 28.0 27.3 12 9.51 702 36 9.54 187 40 10.45813 9.97515 4 48 8 32.8 32.0 31.2 13 9.51 738 36 9.54 228 41 10.45772 9.97510 5 47 9 36.9 36.0 35.1 14 9.51 774 36 9.54 269 41 10.45731 9.97506 4 46 15 9.51 811 37 9.54 309 40 10.45 691 9.97501 5 45 16 9.51 847 36 9.54 350 41 10.45 650 9.97497 4 44 37 36 35 17 9.51 883 36 9.54 390 40 10.45610 9.97492 5 43 18 9.51 919 36 9.54 431 41 10.45 569 9.97488 4 42 2 7.4 7.2 7.0 19 9.51 955 36 9.54 471 40 10.45529 9.97484 i 41 3 11.1 10.8 10.5 20 21 22 23 24 9.51 991 9.52 027 9.52 063 9.52 099 9.52 135 36 36 36 36 36 36 9.54 512 9.54 552 9.54 593 9.54 633 9.54 673 41 40 41 40 40 41 10.45 488 10.45448 10.45 407 10.45 367 10.45 327 9.97479 9.97475 9.97470 9.97466 9.97461 B 4 5 4 5 4 40 39 38 37 36 4 5 6 7 8 9 14.8 18.5 22.2 25.9 29.6 33.3 14.4 18.0 21.6 25.2 28.8 32.4 14.0 17.5 21.0 24.5 28.0 31.5 25 9.52 171 9.54 714 10.45 286 9.97457 35 26 9.52 207 36 9.54 754 40 10.45 246 9.97453 4 34 27 9.52 242 35 9.54 794 40 10.45 206 9.97448 5 33 28 9.52 278 36 9.54 835 41 10.45 165 9.97444 4 32 34 & 4 29 9.52 314 36 9.54 875 40 10.45 125 9.97439 5 31 2 6.8 1.0 0.8 30 9.52 350 36 9.54 915 40 10.45 085 9.97435 4 30 3 10.2 1.5 1.2 31 9.52 385 35 9.54 955 40 10.45 045 9.97430 5 29 4 13.6 2.0 1.6 32 9.52 421 36 9.54 995 40 10.45005 9.97426 4 28 5 17.0 2.5 2.0 33 9.52 456 35 9.55 035 40 10.44965 9.97421 5 27 6 20.4 3.0 2.4 34 9.52 492 36 9.55 075 40 10.44925 9.97417 4 26 7 23.8 3.5 2.8 35 40 5 27.2 4.0 3.2 35 9.52 527 9.55 115 10.44885 9.97412 25 Q A 36 9.52 563 36 9.55 155 40 10.44 845 9.97408 4 24 30. c 4.5 O.D 37 9.52 598 35 9.55 195 40 10.44 805 9.97403 5 23 38 9.52 634 36 9.55 235 40 10.44765 9.97399 4 22 39 9.52 669 35 9.55 275 40 10.44725 9.97 394 5 21 40 9.52 705 36 9.55 315 40 10.44 685 9.97 390 4 20 41 9.52 740 35 9.55 355 40 10.44645 9.97385 5 19 42 9.52 775 35 9.55 395 40 on 10.44 605 9.97381 4 18 From the top: 43 44 9.52811 9.52 846 35 9.55 434 9.55 474 W 40 10.44566 10.44 526 9.97376 9.97372 5 4 17 16 For 19+ or 199+ 45 9.52 881 35 9.55514 40 10.44 486 9.97 367 5 15 read as printed ; for 46 9.52 916 35 9.55 554 40 10.44446 9.97363 4 14 109+or289 0+ ,read 47 9.52 951 35 3C 9.55 593 39 10.44407 9.97358 5 13 co-function. 48 9.52 986 O 9.55 633 40 10.44367 9.97353 5 12 49 50 9.53 021 9.53 056 35 35 9.55 673 9.55 712 40 39 10.44327 10.44 288 9.97349 9.97 344 4 5 11 10 From the bottom: 51 9.53 092 36 9.55 752 40 10.44248 9.97 340 4 9 For 70+ or 250+ 52 53 54 9.53 126 9.53 161 9.53 196 34 35 35 9.55 791 9.55 831 9.55 870 39 40 39 10.44 209 10.44 169 10.44 130 9.97335 9.97331 9.97326 5 4 8 7 6 read as printed ; for 160 0+ or340 0+ ,read 55 9.53 231 35 9.55 910 40 10.44 090 9.97322 4 5 co-function. 56 9.53 266 35 9.55 949 39 10.44051 9.97317 5 4 57 9.53 301 35 9.55 989 40 10.44011 9.97312 5 3 58 9.53 336 35 9.56 028 39 10.43 972 9.97308 4 2 59 9.53 370 34 9.56 067 39 10.43 933 9.97303 5 1 60 9.53 405 35 9.56 107 40 10.43 893 9.97 299 4 LCos d LCtn cd LTan LSin d ' Prop. Pts. 70 Logarithms of Trigonometric Functions 66 20 Logarithms of Trigonometric Functions [III 1 LSin d LTan cd L Ctn LCos d Prop. Pts. 9.53 405 9.56 107 10.43 893 9.97 299 60 1 9.53 440 35 9.56 146 39 10.43 854 9.97 294 5 59 2 9.53 475 35 9.56 185 39 10.43 815 9.97289 5 58 3 9.53 509 34 9.56 224 39 10.43 776 9.97 285 4 57 4 9.53 544 35 9.56 264 40 10.43 736 9.97 280 5 56 5 9.53 578 34 9.56 303 39 10.43 697 9.97 276 4 55 40 39 38 6 9.53 613 35 9.56 342 39 10.43 658 9.97271 5 54 2 8.0 7.8 7.6 7 9.53 647 34 9.56 381 39 10.43 619 9.97 266 53 Q U7 8 9 9.53 682 9.53 716 35 34 35 9.56 420 9.56 459 39 39 39 10.43 580 10.43 541 9.97262 9.97257 4 5 5 52 51 O 4 5 ie!o 20.0 . / 15.6 19.5 15!2 19.0 10 9.53 751 9.56 498 10.43 502 9.97252 50 6 24.0 23.4 22.8 11 9.53 785 34 9.56 537 39 10.43463 9.97 248 4 49 7 28.0 27.3 26.6 12 9.53 819 34 9.56 576 39 10.43 424 9.97243 5 48 8 32.0 31.2 30.4 13 9.53 854 35 9.56615 39 10.43 385 9.97238 5 47 9 36.0 35.1 34.2 14 9.53 888 34 9.56 654 39 10.43 346 9.97 234 4 46 15 9.53 922 34 9.56 693 39 10.43 307 9.97 229 5 45 16 9.53 957 35 9.56 732 39 10.43 268 9.97224 5 44 V7 IK n. 17 9.53 991 34 9.56771 39 10.43 229 9.97 220 4 43 O I Ow O4 18 9.54 025 34 9.56810 39 10.43 190 9.97215 5 42 2 7.4 7.0 6.8 19 9.54 059 34 9.56 849 39 10.43 151 9.97210 5 41 3 11.1 10.5 10.2 20 21 22 23 24 9.54 093 9.54 127 9.54 161 9.54 195 9.54 229 34 34 34 34 34 34 9.56 887 9.56 926 9.56 965 9.57 004 9.57 042 38 39 39 39 38 39 10.43 113 10.43 074 10.43035 10.42996 10.42958 9.97 206 9.97201 9.97 196 9.97 192 9.97 187 4 5 5 4 5 5 40 39 38 37 36 4 5 6 7 8 9 14.8 18.5 22.2 25.9 29.6 33.3 14.0 17.5 21.0 24.5 28.0 31.5 13.6 17.0 20.4 23.8 27.2 30.6 25 9.54 263 9.57 081 10.42919 9.97 182 35 26 9.54 297 34 9.57 120 39 10.42 880 9.97 178 4 34 27 9.54 331 34 9.57 158 38 10.42 842 9.97 173 5 33 28 9.54 365 34 9.57 197 39 10.42 803 9.97 168 5 32 98 4 29 9.54 399 34 9.57 235 38 10.42 765 9.97 163 5 31 2 6.6 1.0 0.8 30 9.54 433 34 9.57 274 39 10.42726 9.97 159 4 30 3 9.9 1.5 1.2 31 9.54 466 33 9.57 312 38 10.42 688 9.97 154 5 29 4 13.2 2.0 1.6 32 9.54 500 34 9.57351 39 10.42 649 9.97 149 5 28 5 16.5 2.5 2.0 33 9.54 534 34 9.57 389 38 10.42611 9.97 145 4 27 6 19.8 3.0 2.4 34 9.54 567 33 9.57 428 39 10.42572 9.97 140 5 26 7 23.1 3.5 2.8 35 36 9.54 601 9.54 635 34 34 9.57 466 9.57 504 38 38 10.42534 10.42496 9.97 135 9.97 130 5 5 25 24 8 9 26.4 29.7 4.0 4.5 3.2 3.6 37 9.54 668 33 9.57 543 39 10.42457 9.97 126 4 23 38 9.54 702 34 9.57 581 38 10.42419 9.97121 5 22 39 9.54 735 33 9.57 619 38 10.42 381 9.97116 5 21 40 9.54 769 34 9.57 658 39 10.42 342 9.97111 5 20 41 9.54 802 33 9.57 696 38 10.42 304 9.97 107 4 19 42 9.54 836 34 9.57 734 38 OQ 10.42 266 9.97 102 5 18 From the top: 43 44 9.54 869 9.54 903 33 34 9.57 772 9.57 810 oo 38 10.42 228 10.42 190 9.97 097 9.97 092 5 17 16 For 20+ or 200+, 45 9.54 936 33 9.57 849 39 10.42 151 9.97 087 5 15 read as printed; for 46 9.54 969 33 9.57 887 38 10.42 113 9.97 083 4 14 110 0+ or290 0+ ,read 47 9.55 003 34 9.57 925 38 oo 10.42075 9.97 078 5 13 co-function. 48 9.55 036 33 9.57 963 OO 10.42 037 9.97073 5 12 49 50 9.55 069 9.55 102 33 33 9.58 001 9.58 039 38 38 10.41 999 10.41 961 9.97068 9.97063 5 5 11 10 From the bottom: 51 9.55 136 34 9.58077 38 10.41 923 9.97059 4 9 For69 0+ or249 0+ , 52 53 54 9.55 169 9.55 202 9.55 235 33 33 33 9.58 115 9.58 153 9.58 191 38 38 38 10.41 885 10.41 847 10.41 809 9.97 054 9.97049 9.97 044 5 5 5 8 7 6 read as printed ; for 159 0+ or339 0+ ,read 55 9.55 268 33 9.58 229 38 10.41 771 9.97039 5 5 co-function. 56 9.55 301 33 9.58 267 38 10.41733 9.97 035 4 4 57 9.55 334 33 9.58 304 37 10.41 696 9.97 030 5 3 58 9.55 367 33 9.58 342 38 10.41 658 9.97 025 5 2 59 9.55 400 33 9.58 380 38 10.41 620 9.97 020 5 1 60 9.55 433 33 9.58418 38 10.41 582 9.97015 5 LCos d LCtn cd LTan LSin d ' Prop. Pts. 69 Logarithms of Trigonometric Functions Ill] 21 Logarithms of Trigonometric Functions 67 ' LSin d LTan cd LCtn LCos d Prop. Pts. 9.55 433 9.58 418 10.41 582 9.97015 60 1 9.55 466 33 9.58 455 37 10.41 545 9.97010 5 59 2 9.55 499 33 9.58 493 38 10.41 507 9.97005 5 58 3 9.55 532 33 9.58531 38 10.41469 9.97001 4 57 4 9.55 564 32 "33 9.58 569 38 37 10.41431 9.96 996 5 5 56 5 9.55 597 Qq 9.58 606 10.41 394 9.96991 55 38 37 36 6 9.55 630 oo qq 9.58644 38 10.41 356 9.96 986 5 54 2 7.6 7.4 7.2 7 9.55 663 OO oo 9.58 681 37 10.41319 9.96 981 5 53 3 1 11.1 10.8 8 9.55 695 Oil 9.58719 38 10.41 281 9.96976 5 52 4. 1 K O 9 9.55 728 33 33 9.58 757 38 37 10.41243 9.96971 5 5 51 rr J.U..4 5 19.0 18.5 is!o 10 9.55 761 9.58 794 10.41 206 9.96966 50 6 22.8 22.2 21.6 11 9.55 793 32 qq 9.58 832 38 10.41 168 9.96 962 4 49 7 26.6 25.9 25.2 12 9.55 826 OO qo 9.58 869 37 10.41 131 9.96957 5 48 8 30.4 29.6 28.8 13 9.55 858 oJ qq 9.58 907 38 10.41 093 9.96 952 5 47 9 34.2 33.3 32.4 14 9.55 891 Oo 9.58 944 37 10.41 056 9.96 947 5 46 15 9.55 923 32 9.58 981 37 10.41 019 9.96 942 5 45 16 9.55 956 33 qo 9.59019 38 10.40981 9.96937 5 44 33 99 91 17 9.55 988 M 9.59 056 37 10.40944 9.96 932 5 43 M M VA 18 9.56 021 33 9.59 094 38 10.40906 9.96 927 5 42 2 6.6 6.4 6.2 19 9.56 053 32 9.59 131 37 10.40869 9.96922 5 41 3 9.9 9.6 9.3 20 21 22 23 24 9.56 085 9.56 118 9.56 150 9.56 182 9.56215 32 33 32 32 33 32 9.59 168 9.59 205 9.59 243 9.59 280 9.59317 37 37 38 37 37 37 10.40832 10.40795 10.40757 10.40720 10.40683 9.96917 9.96912 9.96 907 9.96 903 9.96 898 5 5 5 4 5 5 40 39 38 37 36 4 13.2 5 16.5 6 19.8 7 23.1 8 26.4 9 29.7 12.8 16.0 19.2 22.4 25.6 28.8 12.4 15.5 18.6 21.7 24.8 27.9 25 9.56 247 9.59 354 10.40 646 9.96 893 35 26 .9L5J5279 32 9.59 391 37 10.40609 9.96 888 5 34 27 9.56311 32 9.59 429 38 10.40571 9.96 883 5 33 28 9.56 343 32 9.59466 37 10.40534 9.96 878 5 32 6 5 4 29 9.56 375 32 9.59 503 37 10.40497 9.96873 5 31 2 1.2 1.0 0.8 30 9.56 408 33 9.59 540 37 10.40460 9.96 868 5 30 3 1.8 1.5 1.2 31 9.56 440 32 9.59 577 37 10.40423 9.96863 5 29 4 2.4 2.0 1.6 32 9.56 472 32 9.59 614 37 10.40386 9.96 858 5 28 5 3.0 2.5 2.0 33 9.56 504 32 9.59 651 37 10.40349 9.96 853 5 27 6 3.6 3.0 2.4 34 9.56 536 32 9.59 688 37 10.40312 9.96 848 5 26 7 4.2 3.5 2.8 32 37 5 4B 4 n 39 35 36 9.56 568 9.56 599 31 9.59 725 9.59 762 37 10.40275 10.40 238 9.96843 9.96 838 5 25 24 9 .0 5.4 ^t.w 4.5 ,tj 3.6 37 9.56631 32 9.59 799 37 10.40201 9.96 833 5 23 38 9.56 663 32 9.59 835 36 10.40 165 9.96828 5 22 39 9.56 695 32 32 9.59 872 37 37 10.40 128 9.96823 5 5 21 40 9.56 727 9.59 909 10.40091 9.96818 20 41 9.56 759 32 9.59 946 37 10.40054 9.96813 5 19 42 9.56 790 31 qo 9.59 983 37 10.40017 9.96808 5 18 From the top: 43 44 9.56 822 9.56 854 OM 32 9.60019 9.60 056 36 37 10.39981 10.39944 9.96803 9.96798 5 5 17 16 For21 0+ or201 +, 45 9.56 886 32 9.60 093 37 10.39907 9.96793 5 15 read as printed ; for 46 9.56917 31 9.60 130 37 10.39870 9.96788 5 14 Ill 0+ or291 0+ ,read 47 9.56 949 32 q-i 9.60 166 36 10.39 834 9.96 783 5 13 co-function. 48 9.56 980 ol 9.60 203 37 10.39 797 9.96778 5 12 49 9.57 012 32 9.60 240 37 10.39 760 9.96772 6 11 50 9.57 044 32 9.60 276 36 10.39724 9.96767 5 10 From the bottom: 51 9.57 075 31 9.60313 37 10.39 687 9.96762 5 9 For 68+ or 248+ 52 53 54 9.57 107 9.57 138 9.57 169 31 31 9.60 349 9.60 386 9.60 422 36 37 36 10.39651 10.39 614 10.39 578 9.96757 9.96752 9.96747 5 5 5 8 7 6 read as printed; for 158+ or 338+, read 55 9.57 201 32 9.60459 37 10.39541 9.96742 5 5 co-function. 56 9.57 232 31 9.60 495 36 10.39 505 9.96737 5 4 57 9.57 264 32 9.60532 37 10.39468 9.96732 5 3 58 9.57 295 31 9.60 568 36 10.39 432 9.96727 5 2 59 9.57 326 31 9.60 605 37 10.39 395 9.96722 5 1 60 9.57 358 32 9.60 641 36 10.39 359 9.96717 5 LCos d L Ctn cd L Tan LSin d 1 Prop. Pts. 68 Logarithms of Trigonometric Functions 22 Logarithms of Trigonometric Functions [III 1 LSin d LTan cd LCtn LCos d Prop. Pte. 9.57 358 9.60 641 10.39359 9.96717 60 1 9.57 389 31 9.60 677 36 10.39323 9.96711 59 2 9.57 420 31 9.60714 37 10.39286 9.96 706 5 58 3 9.57451 31 9.60 750 36 10.39250 9.96701 5 57 4 9.57 482 31 9.60 786 36 10.39214 9.96696 56 5 9.57 514 32 9.60 823 37 10.39 177 9.96 691 55 37 36 35 6 7 8 9.57 545 9.57 576 9.57 607 31 31 31 9.60 859 9.60 895 9.60931 36 36 36 10.39 141 10.39 105 10.39 069 9.96 686 9.96681 9.96676 5 6 5 54 53 52 2 3 4 7.4 11.1 Me 7.2 10.8 14 4 7.0 10.5 14 9 9.57 638 31 31 9.60 967 36 37 10.39 033 9.96 670 5 51 5 .0 18.5 Xrt.rr 18.0 i^f\j 17.5 10 9.57 669 9.61 004 10.38996 9.96665 50 G 22.2 21.6 21.0 11 9.57 700 31 9.61 040 36 10.38960 9.96660 49 7 25.9 25.2 24.5 12 9.57 731 31 9.61 076 36 10.38924 9.96655 5 48 8 29.6 28.8 28.0 13 9.57 762 31 9.61 112 36 10.38 888 9.96 650 5 47 9 33.3 32.4 31.5 14 9.57 793 31 9.61 148- 36 10.38852 9.96 646 5 46 15 9.57 824 31 9.61 184 36 10.38816 9.96 640 5 45 16 9.57 855 31 9.61 220 36 10.38780 9.96 634 6 44 oo 31 ^n 17 9.57 885 30 9.61 256 36 10.38 744 9.96629 5 43 38 ol oO 18 9.57 916 31 9.61 292 36 10.38708 9.96 624 5 42 2 6.4 6.2 6.0 19 9.57 947 31 9.61 328 36 10.38672 9.96619 5 41 3 9.6 9.3 9.0 20 21 22 23 24 9.57 978 9.58 008 9.58 039 9.58 070 9.58 101 31 30 31 31 31 30 9.61 364 9.61 400 9.61 436 9.61472 9.61 508 36 36 36 36 36 36 10.38 636 10.38600 10.38 564 10.38528 10.38492 9.96614 9.96608 9.96603 9.96598 9.96593 6 5 B 5 5 40 39 38 37 36 4 5 G 7 8 9 12.8 16.0 19.2 22.4 25.6 28.8 12.4 15.5 18.6 21.7 24.8 27.9 12.0 15.0 18.0 21.0 24.0 27.0 25 9.58 13*1 9.61 544 10.38456 9.96 588 35 26 9.58 162 31 9.61 579 35 10.38421 9.96 582 6 34 27 9.58 192 30 9.61 615 36 10.38385 9.96 577 5 33 28 9.58 223 31 9.61 651 36 10.38349 9.96572 5 32 29 6 5 29 9.58 253 30 9.61 687 36 10.38313 9.96567 5 31 2 5.8 1.2 1.0 30 9.58 284 31 9.61 722 35 10.38 278 9.96 562 5 30 3 8.7 1.8 1.5 31 9.58314 30 9.61 758 36 10.38 242 9.96556 6 29 4 11.6 2.4 2.0 32 9.58 345 31 9.61 794 36 10.38206 9.96551 5 28 5 14.5 3.0 2.5 33 9.58 375 30 9.61 830 36 10.38 170 9.96546 5 27 6 17.4 3.6 3.0 34 9.58 406 31 9.61 865 35 10.38 135 9.96541 5 26 7 20.3 4.2 3.5 30 36 6 97 9 4Q A n 35 36 9.58 436 9.58 467 31 9.61 901 9.61 936 35 10.38 099 10.38 064 9.96 535 9.96530 5 25 24 9 t&*m 26.1 .O 5.4 ^.v/ 4.5 37 9.58 497 30 9.61 972 36 10.38028 9.96525 5 23 38 9.58 527 30 9.62 008 36 10.37 992 9.96520 5 22 39 9.58 557 30 9.62 043 35 10.37 957 9.96514 6 21 40 9.58 588 31 9.62 079 36 10.37 921 9.96 509 5 20 41 9.58618 30 9.62 114 35 10.37 886 9.96504 5 19 42 9.58 648 30 9.62 150 36 3e 10.37 850 9.96498 6 18 From the top: 43 44 9.58 678 9.58 709 30 31 9.62 185 9.62 221 36 10.37815 10.37779 9.96 493 9.96488 5 5 17 16 For22 0+ or202+ 45 9.58 739 30 9.62 256 35 10.37 744 9.96483 5 15 read as printed; for 46 9.58 769 30 9.62 292 36 10.37 708 9.96477 6 14 112 0+ or292+,read 47 9.58 799 30 9.62 327 35 or 10.37 673 9.96472 o 13 co-function. 48 9.58 829 30 9.62 362 BO 10.37638 9.96467 5 12 49 9.58 859 30 9.62 398 36 10.37602 9.96461 6 11 50 9.58 889 30 9.62 433 35 10.37 567 9.96 456 5 10 From the bottom: 51 9.58919 30 9.62 468 35 10.37532 9.96451 5 9 For 67+ or 247+ 52 53 54 9.58 949 9.58 979 9.59 009 30 30 30 9.62 504 9.62 539 9.62 574 35 35 10.37496 10.37461 10.37426 9.96445 9.96440 9.96435 5 5 8 7 6 read as printed; for 157+ or 337+, read 55 9.59 039 30 9.62 609 35 10.37391 9.96429 6 5 co-function. 56 9.59 069 30 9.62 645 36 10.37355 9.96424 5 4 57 9.59 098 29 9.62 680 35 10.37320 9.96419 5 3 58 9.59 128 30 9.62715 35 10.37285 9.96413 6 2 59 9.59 158 30 9.62 750 35 10.37250 9.96408 5 1 60 9.59 188 30 9.62 785 35 10.37 215 9.96403 5 LCos d LCtn cd LTan LSin d ' Prop. Pts. 67 Logarithms of Trigonometric Functions Ill] 23 Logarithms of Trigonometric Functions 69 / LSin d LTan cd L Ctn LCos d Prop. Pts. 9.59 188 9.62 785 10.37 215 9.96403 60 1 9.59 218 30 9.62 820 35 10.37 180 9.96397 6 59 2 9.59 247 29 9.62 855 35 10.37 145 9.96392 5 58 36 35 3 9.59 277 30 9.62 890 35 OA 10.37110 9.96 387 5 57 2 7.2 7.0 4 9.59 307 30 29 9.62 926 OO 35 10.37074 9.96381 5 56 3 10.8 10.5 5 9.59 336 9.62 961 10.37 039 9.96 376 55 4 14.4 14.0 6 9.59 366 30 9.62 996 35 10.37004 9.96370 6 54 5 18.0 17.5 7 9.59 396 30 9.63 031 35 10.36969 9.96365 5 53 6 21.6 21.0 8 9.59 425 29 9.63 066 35 10.36 934 9.96360 5 52 7 25.2 24.5 9 9.59 455 30 9.63 101 35 10.36 899 9.96 354 6 51 8 28.8 28.0 10 9.59 484 29 9.63 135 34 10.36 865 9.96 349 5 50 9 32.4 31.5 11 9.59 514 30 9.63 170 35 10.36 830 9.96343 6 49 12 9.59 543 29 9.63 205 35 10.36 795 9.96338 5 48 nA nt\ 13 9.59 573 30 9.63 240 35 10.36760 9.96333 5 47 M 30 14 9.59 602 29 9.63 275 35 10.36725 9.96327 6 46 2 6.8 6.0 J.5 9.59 632 30 9.63 310 35 10.36 690 9.96 322 5 45 3 10.2 9.0 16 9.59 661 29 9.63 345 35 10.36 655 9.96316 6 44 4 13.6 12.0 17 18 9.59 690 9.59 720 29 30 9.63 379 9.63414 34 35 10.36 621 10.36 586 9.96311 9.96305 5 6 43 42 5 6 17.0 20.4 15.0 18.0 19 9.59 749 29 9.63 449 35 10.36551 9.96300 5 41 7 23.8 21.0 29 35 6 8 27.2 24.0 20 9.59 778 9.63 484 3 10.36516 9.96 294 40 9 30.6 27.0 21 9.59 808 30 9.63519 a 10.36481 9.96 289 39 22 9.59 837 29 9.63 553 34 10.36447 9.96284 5 38 23 9.59 866 29 9.63 588 35 10.36412 9.96 278 6 37 29 28 24 9.59 895 29 29 9.63 623 35 34 10.36 377 9.96 273 5 6 36 2 5.8 5.6 25 9.59 924 OA 9.63 657 oe 10.36 343 9.96 267 35 3 8.7 8.4 26 9.59 954 oU 9.63 692 50 10.36308 9.96 262 34 4 11.6 11.2 27 9.59 983 29 OQ 9.63 726 34 3K 10.36 274 9.96 256 6 33 5 14.5 14.0 28 9.60012 id nr\ 9.63 761 3~ 10.36 239 9.96251 32 6 17.4 16.8 29 9.60 041 fH 29 9.63 796 D 34 10.36 204 9.96 245 5 31 7 20.3 19.6 30 9.60 070 9.63 830 10.36 170 9.96 240 30 8 23.2 22.4 31 9.60 099 29 9.63 865 35 10.36 135 9.96 234 6 29 9 26.1 25.2 32 9.60 128 29 9.63 899 34 10.36 101 9.96229 5 28 33 9.60 157 29 9.63 934 35 10.36066 9.96223 6 27 34 9.60 186 29 9.63 968 34 10.36032 9.96218 5 26 6 5 35 9.60 215 29 9.64 003 35 10.35 997 9.96212 6 25 2 1.2 1.0 36 9.60 244 29 9.64 037 34 10.35 963 9.96207 5 24 3 1.8 1.5 37 9.60 273 29 9.64 072 35 10.35928 9.96201 6 23 4 2.4 2.0 38 9.60 302 29 9.64 106 34 10.35 894 9.96 196 5 22 5 3.0 2.5 39 9.60 331 29 9.64 140 34 10.35 860 9.96 190 6 21 6 3.6 3.0 40 9.60 359 28 9.64 175 35 10.35 825 9.96 185 5 20 7 4.2 3.5 41 9.60 388 29 9.64 209 34 10.35 791 9.96179 6 19 4.8 4.0 42 9.60417 29 9.64 243 34 10.35757 9.96 174 18 9 5.4 4.5 43 9.60 446 29 9.64 278 35 10.35722 9.96 168 C 17 44 9.60 474 28 9.64 312 34 10.35 688 9.96 162 6 16 45 9.60 503 29 9.64 346 34 10.35 654 9.96 157 5 15 From the top: 46 9.60 532 29 9.64 381 35 nt 10.35619 9.96 151 6 14 For 23+ or 203+, 47 48 49 9.60561 9.60 589 9.60618 29 28 29 9.64415 9.64 449 9.64 483 o4 34 34 10.35 585 10.35551 10.35517 9.96 146 9.96 140 9.96135 5 6 5 13 12 11 read as printed; for 113+ or 293+, read 50 9.60 646 28 9.64 517 34 10.35483 9.96 129 6 10 co-function. 51 9.60 675 29 9.64 552 35 10.35448 9.96 123 6 9 52 53 9.60 704 9.60 732 29 28 9.64 586 9.64 620 34 34 10.35414 10.35 380 9.96 118 9.96112 5 6 8 7 From the bottom: 54 9.60 761 29 28 9.64 654 34 34 10.35 346 9.96 107 5 6 6 For 66+ or 246+, 55 56 57 9.60 789 9.60 818 9.60 846 29 28 9.64 688 9.64 722 9.64 756 34 34 10.35312 10.35278 10.35 244 9.96 101 9.96 095 9.96 090 6 5 5 4 3 read as printed; for 156+ or 336+, read 58 9.60 875 29 9.64 790 34 10.35210 9.96084 6 2 co-function. 59 9.60 903 28 28 9.64 824 34 34 10.35 176 9.96079 5 6 1 60 9.60 931 9.64 858 10.35 142 9.96073 LCos d LCtn cd LTan LSin d / Prop. Pts. 66 Logarithms of Trigonometric Functions 70 24 Logarithms of Trigonometric Functions [111 1 LSin d LTan cd L Ctn LCos d Prop. Pts. 9.60 931 9.64 858 10.35 142 9.96073 60 1 9.60 960 29 9.64 892 34 10.35 108 9.96 067 6 59 2 9.60 988 28 9.64 926 34 10.35 074 9.96 062 5 58 34 33 3 9.61 016 28 Ofl 9.64 960 34 O/l 10.35 040 9.96 056 6 57 2 6.8 6.6 4 9.61 045 A) 28 9.64 994 o< 34 10.35 006 9.96 050 6 5 56 3 10.2 9.9 5 9.61 073 9.65 028 10.34 972 9.96 045 55 4 13.6 13.2 6 9.61 101 28 9.65 062 34 10.34938 9.96 039 6 54 5 17.0 16.5 7 9.61 129 28 9.65 096 34 10.34904 9.96 034 5 53 6 20.4 19.8 8 9.61 15' 29 9.65 130 34 10.34870 9.96028 6 52 7 23.8 23.1 9 9.61 186' 28 9.65 164 34 10.34836 9.96022 6 51 8 27.2 26.4 10 9.61 214 28 9.65 197 33 10.34803 9.96017 50 9 30.6 29.7 11 9.61 242 28 9.65 231 34 10.34769 9.96011 6 49 12 9.61 270 28 9.65 265 34 10.34735 9.96005 6 48 on no 13 9.61 298 28 9.65 299 34 10.34701 9.96000 5 47 29 28 14 9.61 326 28 9.65 333 34 10.34 667 9.95 994 6 46 2 5.8 5.6 15 9.61 354 28 9.65 366 33 10.34634 9.95 988 6 45 3 8.7 8.4 16 9.61 382 28 9.65 400 34 10.34600 9.95 982 6 44 4 11.6 11.2 17 9.61411 29 9.65 434 34 10.34566 9.95977 5 43 5 14.5 14.0 18 9.61 438 27 9.65 467 33 10.34533 9.95971 6 42 6 17.4 16.8 19 9.61 466 28 9.65 501 34 10.34499 9.95 965 6 41 7 20.3 19.6 28 34 5 3 23.2 22.4 20 9.61 494 9.65 535 10.34465 9.95 960 40 9 26.1 25.2 21 9.61 522 28 9.65 568 33 10.34432 9.95 954 6 39 22 9.61 550 28 9.65 602 34 10.34398 9.95948 6 38 23 9.61 578 28 9.65 636 34 10.34364 9.95942 6 37 27 6 24 9.61 606 28 28 9.65 669 33 34 10.34331 9.95937 5 6 36 2 5.4 1.2 25 9.61 634 9.65 703 10.34 297 9.95 931 35 3 8.1 1.8 26 9.61 662 28 9.65 736 33 10.34 264 9.95925 6 34 4 io!s 2!4 27 9.61 689 27 9.65 770 34. 10.34 230 9.95 920 5 33 5 13.5 3.0 28 9.61 717 28 9.65 803 33 10.34 197 9.95914 6 32 6 16.2 3.6 29 9.61 745 28 28 9.65 837 34 33 10.34 163 9.95908 6 g 31 7 18.9 4.2 30 9.61 773 9.65 870 10.34 130 9.95 902 30 8 21.6 4.8 31 9.61 800 27 9.65 904 34 10.34 096 9.95 897 5 29 9 24.3 5.4 32 9.61 828 28 9.65 937 33 10.34 063 9.95 891 6 28 33 9.61 856 28 9.65 971 34 10.34029 9.95 885 6 27 34 9.61 883 27 9.66004 33 10.33 996 9.95 879 6 26 5 35 9.61 911 28 9.66 038 34 10.33 962 9.95 873 6 25 2 1.0 36 9.61 939 28 9.66071 33 10.33929 9.95 868 5 24 3 1.5 37 9.61 966 27 9.66 104 33 10.33 896 9.95 862 6 23 4 2.0 38 9.61 994 28 9.66 138 34 10.33862 9.95 856 6 22 6 2.5 39 9.62 021 27 9.66 171 33 10.33 829 9.95 850 6 21 6 3.0 40 9.62 049 28 9.66 204 33 10.33 796 9.95 844 6 20 7 3.5 8 A l\ 41 9.62 076 27 9.66 238 34 10.33762 9.95 839 5 19 4.0 42 9.62 104 28 9.66 271 33 10.33 729 9.95 833 6 18 9 4.5 43 9.62 131 27 9.66 304 33 10.33 696 9.95 827 6 17 44 9.62 159 28 9.66 337 33 10.33 663 9.95 821 6 16 45 9.62 186 27 9.66371 34 10.33 629 9.95 815 6 15 From the top: 46 9.62 214 28 9.66 404 33 10.33596 9.95810 5 14 For 24+ or 204+, 47 48 49 9.62 241 9.62 268 9.62 296 27 27 28 9.66 437 9.66 470 9.66 503 33 33 33 10.33563 10.33530 10.33497 9.95 804 9.95798 9.95792 6 6 6 13 12 11 read as printed ; for 114+ or 294+, read 50 9.62 323 27 9.66 537 34 10.33463 9.95 786 6 10 co-function. 51 9.62 350 27 9.66 570 33 10.33430 9.95780 6 9 52 9.62 377 27 9.66 603 33 10.33 397 9.95775 5 8 53 9.62 405 28 9.66 636 33 10.33 364 9.95 769 7 From the bottom: 54 9.62 432 27 27 9.66 669 33 33 10.33331 9.95763 6 6 6 For65 0+ or245+, 55 56 57 9.62 459 9.62 486 9.62 513 27 27 9.66 702 9.66735 9.66 768 33 33 10.33 298 10.33265 10.33232 9.95757 9.95751 9.95745 G f> 5 4 3 read as printed ; for 155+ or 335+, read 58 9.62 541 28 9.66801 33 10.33 199 9.95739 6 2 co-function. 59 9.62 568 27 9.66 834 33 10.33 166 9.95 733 6 1 60 9.62 595 27 9.66 867 33 10.33 133 9.95 728 5 L Cos d LCtn cd LTan LSin d / Prop. Pts. 65 Logarithms of Trigonometric Functions Ill] 25 Logarithms of Trigonometric Functions 71 ' LSin d LTan cd LCtn LCos d Prop. Pts. 9.62 595 9.66 867 10.33 133 9.95 728 60 1 9.62 622 27 9.66 900 33 10.33 100 9.95 722 6 59 2 9.62 649 27 9.66 933 33 10.33 067 9.95716 6 58 33 32 3 9.62 676 27 9.66 966 33 00 10.33 034 9.95710 6 57 2 6.6 6.4 4 9.62 703 27 27 9.66 999 oo 33 10.33 001 9.95704 6 56 3 9.9 9.6 5 9.62 730 9.67 032 10.32 968 9.95 698 55 4 13.2 12.8 6 9.62 757 27 9.67 065 33 10.32 935 9.95 692 6 54 5 16.5 16.0 7 9.62 784 27 9.67 098 33 10.32 902 9.95 686 6 53 6 19.8 19.2 8 9.62811 27 9.67 131 33 10.32 869 9.95 680 6 52 7 23.1 22.4 9 9.62 838 27 9.67 163 32 10.32837 9.95 674 6 51 8 26.4 25.6 10 9.62 865 27 9.67 196 33 10.32 804 9.95 668 6 50 9 29.7 28.8 11 9.62 892 27 9.67 229 33 10.32771 9.95 663 5 49 12 9.62 918 26 9.67 262 33 10.32738 9.95 657 6 48 fVT e\f 13 9.62 945 27 9.67 295 33 10.32 705 9.95651 6 47 27 26 14 9.62 972 27 9.67 327 32 10.32 673 9.95 645 6 46 2 5.4 5.2 15 9.62 999 27 9.67 360 33 10.32 640 9.95639 6 45 3 8.1 7.8 16 9.63 026 27 9.67 393 33 10.32 607 9.95 633 6 44 4 10.8 10.4 17 9.63 052 26 9.67 426 33 10.32 574 9.95 627 6 43 5 13.5 13.0 18 9.63 079 27 9.67 458 32 10.32 542 9.95621 6 42 6 16.2 15.6 19 9.63 106 27 9.67 491 33 10.32509 9.95 615 6 41 7 18.9 18.2 27 33 6 8 21.6 20.8 20 9.63 133 9.67 524 10.32 476 9.95 609 40 g 24.3 23.4 21 9.63 159 26 9.67 556 32 10.32 444 9.95 603 6 39 22 9.63 186 27 9.67 589 33 10.32411 9.95 597 6 38 23 9.63213 27 9.67 622 33 10.32 378 9.95591 6 37 7 6 24 9.63 239 26 27 9.67 654 32 33 10.32346 9.95 585 6 6 36 2 1.4 1.2 25 9.63 266 9.67 687 oo 10.32313 9.95 579 35 3 2.1 1.8 26 9.63 292 26 9.67719 62 10.32 281 9.95 573 34 4 2.8 2.4 27 9.63 319 27 9.67 752 33 00 10.32 248 9.95567 6 33 5 3.5 3.0 28 9.63 345 26 9.67 785 oo OO 10.32215 9.95561 32 6 4.2 3.6 29 9.63 372 27 26 9.67 817 62 33 10.32 183 9.95 555 6 6 31 7 4.9 4.2 30 9.63 398 9.67850 10.32 150 9.95 549 30 8 5.6 4.8 31 9.63 425 27 9.67 882 32 10.32 118 9.95 543 6 29 9 6.3 5.4 32 9.63 451 26 9.67915 33 10.32 085 9.95537 6 28 33 9.63 478 27 9.67 947 32 10.32 053 9.95531 6 27 34 9.63 504 26 9.67 980 33 10.32 020 9.95525 6 26 5 35 9.63 531 27 9.68 012 32 10.31 988 9.95519 6 25 2 1.0 36 9.63 557 26 9.68 044 32 10.31956 9.95513 6 24 3 1.5 37 9.63 583 26 9.68 077 33 10.31923 9.95507 6 23 4 2.0 38 9.63 610 27 9.68 109 32 10.31891 9.95500 7 22 5 2.5 39 9.63 636 26 9.68 142 33 10.31 858 9.95494 6 21 6 3.0 40 9.63 662 26 9.68 174 32 10.31 826 9.95488 6 20 7 3.5 41 9.63 689 27 9.68 206 32 10.31 794 9.95482 6 19 8 4.0 9 A K. 42 9.63 715 26 9.68 239 33 10.31761 9.95476 6 18 4.5 43 9.63 741 26 9.68271 32 10.31 729 9.95470 6 17 44 9.63 767 26 9.68 303 32 10.31 697 9.95464 6 16 45 9.63 794 27 9.68 336 33 10.31 664 9.95458 6 15 From the top: 46 9.63 820 26 9.68 368 32 Oo 10.31 632 9.95452 6 14 For 25+ or 205+ 47 48 49 9.63 846 9.63 872 9.63 898 26 26 9.68 400 9.68432 9.68 465 O3f 32 33 10.31 600 10.31568 10.31 535 9.95446 9.95440 9.95 434 6 6 13 12 11 read as printed; for 115+ or 295+, read 50 9.63 924 26 9.68 497 32 10.31 503 9.95427 7 10 co-function. 51 9.63 950 26 9.68 529 32 10.31471 9.95421 6 9 52 53 9.63 976 9.64 002 26 26 9.68561 9.68 593 32 32 10.31439 10.31 407 9.95415 9.95409 6 6 8 7 From the bottom: 54 9.64 028 26 26 9.68 626 33 32 10.31 374 9.95403 6 6 6 For 64+ or 244+ 55 56 57 9.64 054 9.64 080 9.64 106 26 26 9.68 658 9.68 690 9.68 722 32 32 10.31 342 10.31310 10.31 278 9.95 397 9.95391 9.95384 6 7 5 4 3 read as printed ; for 154+ or 334+, read 58 9.64 132 26 9.68 754 32 10.31 246 9.95378 6 2 co-function. 59 9.64 158 26 26 9.68 786 32 32 10.31214 9.95 372 6 6 1 60 9.64 184 9.68818 10.31 182 9.95 366 LCos d L Ctn cd L Tan LSin d ' Prop. Pts. 64 Logarithms of Trigonometric Functions 72 26 Logarithms of Trigonometric Functions [III / LSin d LTan cd LCtn LCos d Prop. Pts. 9.64 184 9.68818 10.31 182 9.95 366 60 1 9.64 210 26 9.68 850 32 10.31 150 9.95360 6 59 2 9.64 236 26 9.68882 32 10.31118 9.95 354 6 58 32 31 3 9.64 262 26 nft 9.68914 32 10.31086 9.95 348 G 57 2 6.4 6.2 4 9.64 288 ao 25 9.68 946 32 32 10.31 054 9.95341 6 56 3 9.6 9.3 5 9.64 313 9.68 978 10.31 022 9.95 335 55 4 12.8 12.4 6 9.64 339 26 9.69 010 32 10.30990 9.95329 6 54 5 16.0 15.5 7 9.64 365 26 9.69 042 32 10.30958 9.95323 6 53 6 19.2 18.6 8 9.64-39T . 26 9.69 074 32 10.30926 9.95317 6 52 7 22.4 21.7 9 9.64 417 26 9.69 106 32 10.30894 9.95310 7 51 8 25.6 24.8 10 9.64 442 25 9.69 138 32 10.30862 9.95 304 6 50 9 28.8 27.9 11 9.64 468 26 9.69 170 32 10.30830 9.95 298 6 49 12 9.64 494 26 9.69 202 32 10.30798 9.95 292 6 48 rt/% OC 13 9.64 519 25 9.69 234 32 10.30766 9.95286 6 47 26 25 14 9.64 545 26 9.69 266 32 10.30734 9.95 279 7 46 2 5.2 5.0 15 9.64 571 26 9.69 298 32 10.30 702 9.95 273 6 45 3 7.8 7.5 16 9.64 596 25 9.69 329 31 10.30671 9.95 267 6 44 4 10.4 10.0 17 9.64 622 26 9.69 361 32 10.30 639 9.95 261 6 43 6 13.0 12.5 18 9.64 647 25 9.69 393 32 10.30607 9.95 254 7 42 6 15.6 15.0 19 9.64 673 26 9.69 425 32 10.30575 9.95 248 6 41 7 18.2 17.5 25 32 8 20.8 20.0 20 9.64 698 9.69 457 10.30 543 9.95 242 40 9 23.4 22.5 21 9.64 724 26 9.69 488 31 10.30512 9.95 236 6 39 22 9.64 749 25 9.69 520 32 10.30480 9.95 229 7 38 23 9.64 775 26 9.69 552 32 10.30448 9.95 223 6 37 24 7 24 9.64 800 25 26 9.69 584 32 31 10.30416 9.95217 6 6 36 2 4.8 1.4 25 9.64 826 ne 9.69 615 10.30385 9.95211 35 3 7.2 2.1 26 9.64 851 80 9.69 647 32 10.30353 9.95 204 34 4 9.6 2.8 27 9.64 877 26 9.69 679 32 10.30321 9.95 198 6 33 5 12.0 3.5 28 9.64 902 25 O K 9.69 710 31 10.30290 9.95 192 6 32 6 14.4 4.2 29 9.64 927 M 26 9.69 742 32 32 10.30 258 9.95 185 Q 31 7 16.8 4.9 30 9.64 953 9.69 774 10.30 226 9.95 179 30 8 19.2 5.6 31 9.64 978 25 9.69 805 31 10.30 195 9.95 173 6 29 9 21.6 6.3 32 9.65 003 25 9.69 837 32 10.30 163 9.95 167 6 28 33 9.65 029 26 9.69 868 31 10.30132 9.95 160 7 27 34 9.65 054 25 9.69 900 32 10.30 100 9.95 154 G 26 6 35 9.65 079 25 9.69 932 32 10.30 068 9.95 148 6 25 2 1.2 36 9.65 104 25 9.69 963 31 10.30037 9.95 141 7 24 3 1.8 37 9.65 130 26 9.69 995 32 10.30005 9.95 135 6 23 4 2.4 38 9.65 155 25 9.70 026 31 10.29 974 9.95 129 6 22 6 3.0 39 9.65 180 25 9.70 058 32 10.29 942 9.95 122 7 21 6 3.6 40 9.65 205 25 9.70 089 31 10.29911 9.95116 6 20 7 4.2 8 A Q 41 9.65 230 25 9.70 121 32 10.29 879 9.95110 6 19 4,o 9K A 42 9.65 255 25 9.70 152 31 10.29 848 9.95 103 7 18 5.4 43 9.65 281 26 9.70 184 32 10.29816 9.95 097 6 17 44 45 9.65 306 9.65 331 25 25 9.70 215 9.70 247 31 32 10.29 785 10.29 753 9.95 090 9.95 084 7 6 16 15 From the top: 46 9.65 356 25 9.70 278 31 10.29 722 9.95 078 6 14 For26+or206 +, 47 48 49 9.65 381 9.65 406 9.65 431 25 25 25 9.70 309 9.70 341 9.70 372 31 32 31 10.29691 10.29 659 10.29 628 9.95071 9.95 065 9.95 059 7 6 6 13 12 11 read as printed; for 116 0+ or296 0+ ,read 50 9.65 456 25 9.70 404 32 10.29 596 9.95 052 7 10 co-function. 51 9.65 481 25 9.70435 31 10.29 565 9.95046 6 9 52 53 9.65 506 9.65531 25 25 9.70 466 9.70 498 31 32 10.29 534 10.29502 9.95039 9.95 033 7 G 8 7 From the bottom: 54 9.65 556 25 24 9.70 529 31 31 10.29471 9.95 027 6 7 6 For63+or243 0+ , 55 56 57 9.65 580 9.65 605 9.65 630 25 25 9.70 560 9.70 592 9.70 623 32 31 10.29 440 10.29408 10.29 377 9.95 020 9.95014 9.95007 G 7 5 4 3 read as printed; for 153+ or 333+, read 58 9.65 655 25 9.70 654 31 10.29 346 9.95001 6 2 co-function. 59 9.65 680 25 25 9.70 685 31 32 10.29315 9.94 995 6 7 1 60 9.65 705 9.70717 10.29 283 9.94 988 LCos d LCtn cd LTan LSin d / Prop. Pts. 63 Logarithms of Trigonometric Functions Ill] 27 Logarithms of Trigonometric Functions 73 / LSin d LTan cd L Ctn L Cos d Prop. Pts. 9.65 705 9.70717 10.29 283 9.94 988 60 1 9.65 729 24 9.70 748 31 10.29252 9.94 982 6 59 a 9.65 754 25 9.70 779 31 10.29221 9.94975 7 58 32 31 3 9.65 779 25 9.70810 31 10.29 190 9.94969 6 57 2 6.4 6.2 4 9.65 804 25 24 9.70841 31 32 10.29 159 9.94962 7 6 56 3 9.6 9.3 5 9.65 828 9.70 873 10.29 127 9.94956 55 4 12.8 12.4 6 9.65 853 25 9.70 904 31 10.29 096 9.94949 7 54 5 16.0 15.5 7 9.65 878 25 9.70 935 31 10.29065 9.94943 6 53 6 19.2 18.6 8 9.65 902 24 9.70 966 31 10.29 034 9.94936 7 52 7 22.4 21.7 9 9.65 927 25 9.70 997 31 10.29 003 9.94930 6 51 8 25.6 24.8 10 9.65 952 25 9.71 028 31 10.28 972 9.94923 7 50 9 28.8 27.9 11 9.65 976 24 9.71 059 31 10.28941 9.94917 6 49 12 9.66 001 25 9.71 090 31 10.28910 9.94911 6 48 f)f\ e\r* 13 9.66 025 24 9.71 121 31 10.28879 9.94904 7 47 30 B 14 9.66 050 25 9.71 153 32 10.28847 9.94898 6 46 2 6.0 5.0 15 9.66 075 25 9.71 184 31 10.28816 9.94891 7 45 3 9.0 7.5 1C 9.66 099 24 9.71215 31 10.28 785 9.94885 6 44 4 12.0 10.0 17 9.66 124 25 9.71 246 31 10.28754 9.94878 7 43 5 15.0 12.5 18 9.66 148 24 9.71277 31 10.28723 9.94871 7 42 6 18.0 15.0 19 9.66 173 25 9.71 308 31 10.28 692 9.94 865 6 41 7 21.0 17.5 24 31 7 8 24.0 20.0 20 9.66 197 9.71 339 10.28661 9.94858 40 9 27.0 9.9. .5 21 9.66 221 24 9.71 370 31 10.28630 9.94 852 6 39 22 9.66 246 25 9.71 401 31 10.28 599 9.94845 7 38 23 9.66 270 24 9.71 431 30 10.28569 9.94839 6 37 24 23 24 9.66 295 25 24 9.71 462 31 31 10.28538 9.94 832 7 6 36 2 4.8 4.6 25 9.66319 9.71 493 10.28507 9.94 826 35 3 7.2 6.9 26 9.66 343 24 9.71 524 31 10.28476 9.94819 7 34 4 9.6 9.2 27 9.66 368 25 9.71 555 31 10.28445 9.94813 6 33 5 12.0 11.5 28 9.66 392 24 9.71 586 31 10.28414 9.94 806 7 32 6 14.4 13.8 29 9^6 416 24 25 9.71 617 31 31 10.28383 9.94799 7 6 31 7 16.8 16.1 30 9.66 441 9.71 648 10.28 352 9.94793 30 8 19.2 18.4 31 9.66 465 24 9.71 679 31 10.28321 9.94786 7 29 9 21.6 20.7 32 9.66 489 24 9.71 709 30 10.28291 9.94780 6 28 33 9.66513 24 9.71 740 31 10.28260 9.94773 7 27 34 9.66 537 24 9.71 771 31 10.28229 9.94767 6 26 7 6 35 9.66 562 25 9.71 802 31 10.28 198 9.94760 7 25 2 1.4 1.2 36 9.66 586 24 9.71 833 31 10.28 167 9.94753 7 24 3 2.1 1.8 37 9.66 610 24 9.71 863 30 10.28 137 9.94747 6 23 4 2.8 2.4 38 9.66 634 24 9.71 894 31 10.28 106 9.94 740 7 22 6 3.5 3.0 39 9.66 65,8 24 9.71 925 31 10.28075 9.94734 6 21 6 4.2 3.6 40 9.66 682 24 9.71 955 30 10.28 045 9.94727 7 20 7 4.9 4.2 41 9.66 706 24 9.71 986 31 10.28014 9.94 720 7 19 J 5.6 4.8 42 9.66 731 25 9.72 017 31 10.27983 9.94714 6 18 9 6.3 5.4 43 9.66 755 24 9.72 048 31 10.27952 9.94707 7 17 44 9.66 779 24 9.72 078 30 10.27922 9.94700 7 16 45 9.66 803 24 9.72 109 31 10.27891 9.94 694 6 15 From the top: 46 9.66 827 24 9.72 140 31 nf\ 10.27 860 9.94 687 7 14 For 27+ or 207+, 47 48 49 9.66 851 9.66 875 9.66 899 24 24 24 9.72 170 9.72 201 9.72 231 OU 31 30 10.27830 10.27799 10.27769 9.94 680 9.94 674 9.94667 7 6 7 13 12 11 read as printed; for 117-*- or 297+ read 50 9.66 922 23 9.72 262 31 10.27 738 9.94 660 7 10 co-function. 51 9.66 946 24 9.72 293 31 10.27707 9.94 654 6 9 52 9.66 970 24 9.72 323 30 10.27 677 9.94 647 7 8 53 9.66 994 24 9.72 354 31 10.27 646 9.94640 7 7 From the bottom: 54 9.67 018 24 24 9.72 384 30 31 10.27616 9.94 634 6 7 6 For 62+ or 242+ 55 56 57 9.67 042 9.67 066 9.67 090 24 24 9.72 415 9.72 445 9.72 476 30 31 10.27585 10.27555 10.27524 9.94627 9.94 620 9.94614 7 6 5 4 3 read as printed; for 152+ or 332+, read 58 9.67113 23 9.72 506 30 10.27494 9.94 607 7 2 co-function. 59 9.67 137 24 9.72 537 31 10.27 463 9.94600 7 1 60 9.67161 24 9.72 567 30 10.27433 9.94 593 7 LCos d LCtn cd LTan LSin d i Prop. Pts. 62 Logarithms of Trigonometric Functions 74 28 Logarithms of Trigonometric Functions [III 1 LSin d LTan cd LCtn L Cos d Prop. Pts. 9.67 161 9.72 567 10.27433 9.94 593 60 1 9.67 185 24 9.72 598 31 10.27402 9.94 587 6 59 2 9.67 208 23 9.72 628 30 10.27372 9.94 580 7 58 31 30 3 9.67 232 24 9.72 659 31 10.27341 9.94573 7 57 2 6.2 6.0 4 9.67 256 24 24 9.72 689 30 31 10.27311 9.94567 6 7 56 3 9.3 9.0 5 9.67 280 9.72 720 10.27 280 9.94560 55 4 12.4 12.0 6 9.67 303 23 9.72 750 30 10.27 250 9.94553 7 54 5 15.5 15.0 7 9.67 327 24 9.72 780 30 10.27 220 9.94546 7 53 6 18.6 18.0 8 9.67 350 23 9.72811 31 10.27 189 9.94 540 6 52 7 21.7 21.0 9 9.67 374 24 9.72 841 30 10.27 159 9.94533 7 51 8 24.8 24.0 10 9.67 398 24 9.72 872 31 10.27 128 9.94 526 7 50 9 27.9 27.0 11 9.67 421 23 9.72 902 30 10.27 098 9.94519 7 49 12 9.67 445 24 9.72 932 30 10.27068 9.94513 6 48 f\r\ t~* * 13 9.67 468 23 9.72 963 31 10.27037 9.94 506 7 47 M iM 14 9.67 492 24 9.72 993 30 10.27007 9.94499 7 46 2 5.8 4.8 15 9.67 SiS 23 9.73 023 30 10.26977 9.94492 7 45 3 8.7 7.2 - 16 9.67 539 24 9.73 054 31 10.26946 9.94485 7 44 4 11.6 9.6 17 9.67 562 23 9.73 084 30 10.26916 9.94479 6 43 5 14.5 12.0 18 9.67 586 24 9.73114 30 10.26886 9.94472 7 42 6 ft ~ 17.4 14.4 19 9.67 609 23 9.73 144 30 10.26 856 9.94465 7 41 7 20.3 16.8 20 9.67 633 24 9.73 175 31 10.26825 9.94 458 7 40 8 9 26.1 91.fi 21 9.67 656 23 9.73 205 30 10.26795 9.94451 7 39 22 9.67 680 24 9.73 235 30 10.26 765 9.94 445 6 38 23 9.67 703 23 9.73 265 30 10.26 735 9.94438 7 37 23 22 24 9.67 726 23 24 9.73 295 30 31 10.26 705 9.94431 7 7 36 2 4.6 4.4 25 9.67 750 9.73 326 10.26 674 9.94424 35 3 6.9 6.6 26 9.67 773 23 9.73 356 30 10.26 644 9.94417 7 34 4 9.2 8.8 27 9.67 796 23 9.73 386 30 10.26 614 9.94410 7 33 5 11.5 11.0 28 9.67 820 24 9.73 416 30 10.26 584 9.94 404 6 32 6 13.8 13.2 29 9.67 843 23 23 9.73 446 30 30 10.26 554 9.94397 7 7 31 7 16.1 15.4 30 9.67 866 9.73 476 10.26 524 9.94 390 30 8 18.4 17.6 31 9.67 890 24 9.73 507 31 10.26493 9.94 383 7 29 9 20.7 19.8 32 9.67913 23 9.73 537 30 10.26463 9.94376 7 28 33 9.67 936 23 9.73 567 30 10.26433 9.94 369 7 27 34 9.67 959 23 9.73 597 30 10.26403 9.94362 7 26 7 6 35 9.67 982 23 9.73 627 30 10.26 373 9.94 355 7 25 2 1.4 1.2 30 9.68 006 24 9.73 657 30 10.26 343 9.94 349 6 24 3 2.1 1.8 37 9.68 029 23 9.73 687 30 10.26313 9.94342 7 23 4 2.8 2.4 38 9.68 052 23 9.73 747 30 10.26283 9.94335 7 22 5 3.5 3.0 39 9.68 075 23 9.73 747 30 10.26 253 9.94328 7 21 6 4.2 3.6 40 9.68 098 23 9.73 777 30 10.26 223 9.94321 7 20 7 4.9 K A 4.2 40 41 9.68 121 23 9.73 807 30 10.26 193 9.94314 7 19 5.D .0 42 9.68 144 23 9.73 837 30 10.26 163 9.94307 7 18 9 6.3 S.4 43 9.68 167 23 9.73 867 30 10.26 133 9.94300 7 17 44 9.68 190 23 9.73 897 30 10.26 103 9.94 293 7 16 45 9.68 213 23 9.73 927 30 10.26073 9.94 286 7 15 From the top: 46 9.68 237 24 9.73 957 30 10.26043 9.94279 7 14 For 28+ or 208+ 47 48 49 9.68 260 9.68 283 9.68 3Q 23 23 22 9.73 987 9.74 017 9.74 047 30 30 30 10.26013 10.25 983 10.25 953 9.94 273 9.94 266 9.94_259_ 6 7 7, 13 12 11 read as printed; for 118 - 1 - or 298+ read 50 9.68 328 23 9.74 077 30 10.25 923 9.94 252 7 10 co-function. 51 9.68 351 23 9.74 107 30 10.25 893 9.94245 7 9 52 53 9.68 374 9.68 397- 123 23 9.74 137. 9.74 166 30 29 10.25 863 10.25 834 9.94238 9.94231 7 7 8 7 From the bottom: 54 9.68 420 23 23 9.74 196 30 30 10.25 804 9.94224 7 7 6 For 61 - 1 - or 241+, 55 56 57 9.68 443 9.68 466 9.68 489 23 23 9.74 226 9.74 256 9.74 286 30 30 10.25 774 10.25744 10.25714 9.94217 9.94210 9.94203 7 7 5 4 3 read as printed; for 151+ or 331+ read 58 9.68512 23 oo 9.74 316 30 10.25 684 9.94 196 7 2 co-function. 59 9.68 534 yz 9.74 345 29 10.25655 9.94 189 7 1 60 9.68 557 23 9.74 375 30 10.25 625 9.94 182 7 LCos d LCtn cd L Tan LSin d ' Prop. Pts. 61 Logarithms of Trigonometric Functions Ill] 29 Logarithms of Trigonometric Functions 75 1 LSin d LTan cd L Ctn LCos d Prop. Pts. 9.68 557 9.74 375 10.25 625 9.94 182 60 1 9.68 580 23 9.74 405 30 10.25595 9.94 175 7 59 . 2 9.68 603 23 9.74 435 30 10.25 565 9.94 168 7 58 -U 3 9.68 625 22 9.74 465 30 10.25 535 9.94 161 7 57 "^jO 4 9.68 648 23 9.74 494 29 10.25 506 9.94 154 7 56 IX 23 30 7 5 9.68671 9.74 524 10.25 476 9.94 147 55 30 29 6 9.68 694 23 9.74 554 30 10.25 446 9.94 140 7 54 2 Go K Q 7 9.68716 22 9.74 583 29 10.25417 9.94 133 7 53 o \j 9n O.O c 7 - 8 9.68 739 23 9.74 613 30 10.25 387 9.94 126 7 52 o 4 u 12.0 O. 1 Uft 9 9.68 762 23 22 9.74 643 30 30 10.25 357 9.94119 7 7 51 5 isio .w 14.5 10 9.68 784 9.74 673 10.25 327 9.94112 50 6 18.0 17.4 11 9.68 807 23 9.74 702 29 10.25 298 9.94 105 7 49 7 21.0 20.3 12 9.68 829 22 9.74 732 30 10.25 268 9.94098 7 48 8 24.0 23.2 13 9.68 852 23 r>o 9.74 762 30 10.25 238 9.94 090 8 47 9 27.0 26.1 14 9.68 875 M 9.74 791 29 10.25 209 9.94083 7 46 15 9.68 897 22 9.74 821 30 10.25 179 9.94 076 7 45 16 9.68 920 23 9.74851 30 10.25 149 9.94 069 7 44 oo 99 17 9.68 942 22 9.74 880 29 10.25 120 9.94 062 7 43 BB 10% 18 9.68 965 23 9.74 910 30 10.25 090 9.94 055 7 42 2 4.6 4.4 19 9.68 987 22 9.74 939 29 10.25 061 9.94 048 7 41 3 6.9 6.6 20 9.69 010 23 9.74 969 30 10.25031 9.94 041 7 40 4 9.2 nc 8.8 nr 21 22 9.69 032 9.69 055 22 23 9.74 998 9.75 028 29 30 10.25 002 10.24 972 9.94 034 9.94 027 7 7 39 38 6 .0 13.8 1 /> ~t U 13.2 f C A 23 9.69 077 22 9.75 058 30 10.24 942 9.94 020 7 37 lO.l TO 4 15.4 17 fi 24 9.69 100 23 22 9.75 087 29 30 10.24913 9.94012 8 7 36 9 AO,*! 20.7 . 4 ,\J 19.8 25 9.69 122 9.75 117 10.24 883 9.94005 35 26 9.69 144 22 9.75 146 29 10.24 854 9.93 998 7 34 27 9.69 167 23 9.75 176 30 10.24 824 9.93 991 7 33 28 9.69 189 22 9.75 205 29 10.24 795 9.93 984 7 32 8 7 29 9.69 212 23 9.75 235 30 10.24765 9.93 977 7 31 2 1.6 1.4 30 9.69 234 22 9.75 264 29 10.24 736 9.93 970 7 30 3 2.4 2.1 31 9.69 256 22 9.75 294 30 10.24706 9.93 963 7 29 4 3.2 2.8 32 9.69 279 23 9.75 323 29 10.24 677 9.93 955 8 28 5 4.0 3.5 33 9.69 301 22 9.75 353 30 10.24 647 9.93 948 7 27 6 4.8 4.2 34 9.69 323 22 9.75 382 29 10.24 618 9.93 941 7 26 7 5.6 4.9 35 36 9.69 345 9.69 368 22 23 9.75411 9.75 441 29 30 10.24 589 10.24559 9.93 934 9.93927 7 7 25 24 8 9 6.4 7.2 5.6 6.3 37 9.69 390 22 9.75 470 29 10.24530 9.93 920 7 23 38 9.69412 22 9.75 500 30 10.24 500 9.93912 8 22 39 9.69 434 22 9.75 529 29 10.24471 9.93 905 7 21 40 9.69 456 22 9.75 558 29 10.24442 9.93 898 7 20 41 9.69 479 23 9.75 588 30 10.24412 9.93 891 7 19 42 9.69 501 22 9.75 617 29 10.24 383 9.93 884 7 18 From the top: 43 44 9.69 523 9.69 545 22 22 9.75 647 9.75 676 30 29 10.24 353 10.24324 9.93 876 9.93 869 8 7 17 16 For29 0+ or209 0+ , 45 9.69 567 22 9.75 705 29 10.24 295 9.93 862 7 15 read as printed; for 46 9.69 589 22 9.75 735 30 10.24 265 9.93 855 7 14 119+ or 299 - 1 -, read 47 9.69 611 22 9.75 764 29 10.24236 9.93 847 8 13 co-function. 48 9.69 633 22 9.75 793 29 10.24207 9.93 840 7 12 49 9.69 655 22 9.75 822 29 10.24178 9.93 833 7 11 50 9.69 677 22 9.75 852 30 10.24 148 9.93 826 7 10 From the bottom: 51 9.69 699 22 9.75 881 29 10.24119 9.93819 7 9 For60 + or240 0+ , 52 53 54 9.69 721 9.69 743 9.69 765 22 22 22 9.75 910 9.75 939 9.75 969 29 29 30 10.24090 10.24061 10.24031 9.93811 9.93 804 9.93797 8 7 7 8 7 6 read as printed; for 150+ or 330+, read 55 9.69 787 22 9.75 998 29 10.24 002 9.93 789 S 5 co-function. 56 9.69 809 22 9.76 027 29 10.23 973 9.93782 7 4 57 9.69 831 22 9.76 056 29 10.23 944 9.93775 7 3 58 9.69 853 22 9.76 086 30 10.23914 9.93 768 7 o 59 9.69 875 22 9.76 115 29 10.23 885 9.93 760 S 1 60 9.69 897 22 9.76 144 29 10.23 856 9.93 753 7 LCos d LCtn cd LTan LSin d ' Prop. Pts. 60 Logarithms of Trigonometric Functions 76 30 Logarithms of Trigonometric Functions [ill / LSin d LTan cd LCtn L Cos d Prop. Pts. 9.69 897 9.76 144 10.23 856 9.93 753 60 1 9.69 919 22 9.76 173 29 10.23 827 9.93 746 7 59 2 9.69 941 22 9.76 202 29 10.23 798 9.93738 8 58 30 29 3 9.69 963 22 9.76231 29 10.23 769 9.93731 7 57 2 6 5 8 4 9.69 984 21 22 9.76 261 30 29 10.23 739 9.93 724 7 7 56 3 9.0 8.7 5 9.70 006 9.76 290 10.23 710 9.93 717 55 4 12.0 11.6 6 9.70 028 22 9.76319 29 10.23 681 9.93709 8 54 5 15.0 14.5 7 9.70 050 22 9.76 348 29 10.23 652 9.93702 7 53 6 18.0 17.4 8 9.70 072 22 9.76 377 29 10.23 623 9.93 695 7 52 7 21.0 20.3 9 9.70 093 21 9.76 406 29 10.23 594 9.93 687 8 51 8 24.0 23.2 10 9.70 115 22 9.76 435 29 10.23 565 9.93 680 7 50 9 27.0 26.1 11 9.70 137 22 9.76 464 29 10.23 536 9.93 673 7 49 12 9.70 159 22 9.76 493 29 10.23 507 9.93665 8 48 13 9.70 180 21 9.76 522 29 10.23478 9.93 658 7 47 ao 2EI 14 9.70 202 22 9.76551 29 10.23 449 9.93 650 8 46 2 5.6 4.4 15 9.70 224 22 9.76 580 29 10.23 420 9.93 643 7 45 3 8.4 6.6 16 9.70 245 21 9.76 609 29 10.23 391 9.93 636 7 44 4 11.2 8.8 17 9.70 267 22 9.76 639 30 10.23 361 9.93 628 8 43 5 14.0 11.0 18 9.70 288 21 9.76 668 29 10.23 332 9.93 621 7 42 6 16.8 13.2 19 9.70 310 22 9.76 697 29 10.23 303 9.93 614 7 41 7 19.6 15.4 22 28 g g 22 4. 17.6 20 9.70 S32 9.76 725 10.23 275 9.93 606 40 9 9K 9 1Q 21 9.70 353 21 9.76 754 29 10.23 246 9.93 599 7 39 22 9.70 375 22 9.76 783 29 10.23217 9.93591 8 38 23 9.70 396 21 9.76812 29 10.23 188 9.93 584 7 37 21 8 24 9.70 418 22 21 9.76 841 29 29 10.23 159 9.93 577 7 8 36 2 4.2 1.6 25 9.70 439 9.76 870 10.23 130 9.93 569 35 3 6.3 2.4 26 9.70461 22 9.76 899 29 10.23 101 9.93 562 7 34 4 8.4 3.2 27 9.70 482 21 9.76 928 29 10.23 072 9.93 554 8 33 5 10.5 4.0 28 9.70 504 22 9.76 957 29 10.23 043 9.93 547 7 32 6 12.6 4.8 29 9.70 525 21 22 9.76 986 29 29 10.23014 9.93 539 8 7 31 7 14.7 5.6 30 9.70 547 9.77 015 10.22 985 1 9.93 532 30 8 16.8 6.4 31 9.70 568 21 9.77 044 29 10.22956 9.93 525 7 29 9 18.9 7.2 32 9.70 590 22 9.77 073 29 10.22 927 9.93517 8 28 33 9.70611 21 9.77 101 28 10.22 899 9.93 510 7 27 34 9.70 633 22 9.77 130 29 10.22 870 9.93502 8 26 7 35 9.70 654 21 9.77 159 29 10.22 841 9.93495 7 25 2 1.4 36 9.70 675 21 9.77 188 29 10.22812 9.93487 8 24 3 2.1 37 9.70 697 22 9.77217 29 10.22 783 9.93 480 7 23 4 2.8 38 9.70718 21 9.77 246 29 10.22 754 9.93472 8 22 5 3.5 39 9.70 739 21 9.77 27.4 28 10.22 726 9.93465 7 21 6 4.2 40 9.70 761 22 9.77 3t>3 29 10.22 697 9.93 457 8 20 7 4.9 41 9.70 782 21 9.77 332 29 10.22668 9.93450 7 19 8 5.6 42 9.70 803 21 9.77361 29 10.22639 9.93442 8 18 9 6.3 43 9.70 824 21 9.77 390 29 10.22610 9.93435 7 17 44 9.70 846 22 9.77418 28 10.22582 9.93427 8 16 45 9.70 867 21 9.77 447 29 10.22553 9.93 420 7 15 From the top: 46 9.70 888 21 01 9.77 476 29 10.22524 9.93412 8 14 For 30+ or 210+, 47 48 49 9.70 909 9.70931 9.70 952 Sfl 22 21 9.77 505 9.77 533 9.77 562 29 28 29 10.22495 10.22467 10.22438 9.93 405 9.93 397 9.93 390 7 8 7 13 12 11 read as printed ; for 120+ or 300+, read 50 9.70 973 21 9.77 591 29 10.22409 9.93 382 8 10 co-function. 51 9.70 994 21 9.77619 28 10.22381 9.93375 7 9 52 9.71 015 21 9.77 648 29 10.22352 9.93 367 8 8 53 9.71 036 21 9.77 677 29 10.22323 9.93 360 7 7 From the bottom: 54 9.71 058 22 21 9.77 706 29 28 10.22294 9.93352 8 g 6 For59 0+ or239 0+ , 55 56 57 9.71 079 9.71 100 9.71 121 21 21 9.77 734 9.77 763 9.77 791 29 28 10.22266 10.22237 10.22209 9.93 344 9.93 337 9.93 329 7 8 5 4 3 read as printed ; for 149+ or 329+, read 58 9.71 142 21 9.77 820 29 10.22 180 9.93322 7 2 co-function. 59 9.71 163 21 9.77 849 29 10.22151 9.93314 8 1 60 9.71 184 21 9.77 877 28 10.22 123 9.93 307 7 LCos d LCtn cd LTan LSin d / Prop. Pts. 59 Logarithms of Trigonometric Functions Ill] 31 Logarithms of Trigonometric Functions 77 ' LSin d LTan cd L Ctn LCos d Prop. Pis. 9.71 184 9.77 877 10.22 123 9.93 307 60 1 9.71 205 21 9.77 906 29 10.22 094 9.93 299 8 59 2 9.71 226 21 9.77 935 29 10.22065 9.93 291 S 58 3 9.71 247 21 9.77 963 28 10.22 037 9.93 284 7 57 4 9.71 268 21 9.77 992 29 10.22 008 9.93276 8 56 5 9.71 289 21 9.78 020 28 10.21 980 9.93 269 7 55 29 28 6 9.71310 21 9.78 049 29 10.21951 9.93 261 8 54 2 5.8 5.6 7 9.71 331 21 9.78 077 28 10.21 923 9.93 253 53 3 8.7 8.4 8 9.71 352 21 9.78 106 29 10.21 894 9.93 246 7 52 4 11.2 9 9.71 373 21 20 9.78 135 29 28 10.21 865 9.93 238 S 51 5 14'.5 u!o 10 9.71 393 9.78 163 10.21 837 9.93 230 50 6 17.4 16.8 11 9.71414 21 9.78 192 29 10.21 808 9.93 223 7 49 7 20.3 19.6 12 9.71 435 21 9.78 220 28 10.21 780 9.93215 8 48 8 23.2 22.4 13 9.71 456 21 9.78 249 29 10.21751 9.93 207 S 47 9 26.1 25.2 14 9.71 477 21 21 9.78 277 28 29 10.21 723 9.93200 7 8 46 15 9.71 498 9.78 306 10.21 694 9.93 192 45 16 9.71519 21 9.78 334 28 10.21 666 9.93 184 8 44 91 9fl 17 9.71 539 20 9.78 363 29 10.21 637 9.93 177 7 43 lU JM IS 9.71 560 21 9.78 391 28 10.21 609 9.93 169 8 42 2 4.2 4.0 19 9.71 581 21 9.78419 28 10.21 581 9.93 161 S 41 3 6.3 6.0 21 29 7 4 8 4 8.0 20 21 22 23 9.71 602 9.71 622 9.71 643 9.71 664 20 21 21 9.78 448 9.78 476 9.78 505 9.78 533 28 29 28 10.21 552 10.21 524 10.21 495 10.21467 9.93 154 9.93 146 9.93 138 9.93 131 S S 7 40 39 38 37 5 6 7 g lo'.s 12.6 14.7 IRC io!o 12.0 14.0 24 9.71 685 21 20 9.78 562 29 28 10.21438 9.93 123 8 8 36 9 xu.o 18.9 is!o 25 9.71 705 9.78 590 10.21410 9.93 115 35 20 9.71 726 21 9.78618 28 10.21 382 9.93 108 7 34 27 9.71 747 21 9.78 647 29 10.21 353 9.93 100 8 33 28 9.71 767 20 9.78 675 28 10.21325 9.93 092 S 32 8 7 29 9.71 788 21 9.78 704 29 10.21 296 9.93 084 8 31 2 1.6 1.4 30 9.71 809 21 9.78 732 28 10.21 268 9.93 077 7 30 3 2.4 2.1 31 9.71 829 20 9.78 760 28 10.21 240 9.93 069 8 29 4 3.2 2.8 32 9.71 850 21 9.78 789 29 10.21211 9.93 061 8 28 5 4.0 3.5 33 9.71 870 20 9.78 817 28 10.21 183 9.93053 S 27 6 4.8 4.2 34 9.71 891 21 9.78 845 28 10.21 155 9.93 046 7 26 7 5.6 4.9 ' 35 9.71911 20 9.78 874 29 10.21 126 9.93 038 S 25 8 6.4 *7 O 5.6 * O 36 9.71 932 21 9.78 902 28 10.21 098 9.93 030 8 24 7.2 o.o 37 9.71 952 20 9.78 930 28 10.21 070 9.93022 8 23 38 9.71 973 21 9.78 959 29 10.21 041 9.93 014 S 22 39 9.71 994 21 9.78 987 28 10.21013 9.93007 7 21 40 9.72 014 20 9.79 015 28 10.20985 9.92999 8 20 41 9.72 034 20 9.79 043 28 10.20957 9.92991 8 19 42 9.72 055 21 9.79 072 29 10.20928 9.92 983 S 18 From the top: 43 44 9.72 075 9.72 096 20 21 9.79 100 9.79 128 28 28 10.20900 10.20872 9.92976 9.92 968 7 8 17 16 For31 0+ or211- | - ) 45 9.72 116 20 9.79 156 28 10.20844 9.92960 8 15 read as printed; for 46 9.72 137 21 9.79 185 29 10.20815 9.92952 8 14 121+ or 301+, read 47 9.72 157 20 9.79 213 28 OQ 10.20787 9.92 944 8 13 co-function. 48 9.72177 2(J 9.79 241 Ja 10.20759 9.92 936 8 12 49 9.72 198 21 9.79 269 28 10.20731 9.92929 7 11 50 9.72 218 20 9.79 297 28 10.20703 9.92 921 S 10 From the bottom: 51 9.72 238 20 01 9.79 326 29 10.20674 9.92913 8 9 For58+or238 0+ , 52 53 54 9.72 259 9.72 279 9.72 299 21 20 20 9.79 354 9.79 382 9.79410 28 28 10.20646 10.20618 10.20 590 9.92905 9.92 897 9.92 889 8 8 S 8 7 6 read as printed ; for 148+ or 328 - 1 -, read 55 9.72 320 21 9.79 438 28 10.20562 9.92 881 8 5 co-function. 56 9.72 340 20 9.79 466 28 10.20534 9.92 874 7 4 57 9.72 360 20 9.79 495 29 10.20505 9.92 866 8 3 58 9.72 381 21 9.79 523 28 10.20477 9.92858 S 2 59 9.72 401 20 20 9.79 551 28 28 10.20449 9.92 850 8 8 1 60 9.72 421 9.79 579 10.20421 9.92 842 LCos d LCtn cd LTan LSin d ' Prop. Pts. 58 Logarithms of Trigonometric Functions 78 32 Logarithms of Trigonometric Functions [III ' LSin d LTan cd L Ctn L Cos d Prop. Pts. 9.72421 9.79 579 10.20421 9.92842 60 1 9.72 441 20 9.79 607 28 10.20393 9.92834 8 59 2 9.72 461 20 9.79 635 28 10.20365 9.92826 8 58 29 28 3 9.72 482 21 9.79 663 28 10.20337 9.92818 8 57 2 5.8 5.6 4 9.72 502 20 20 9.79 691 28 28 10.20309 9.92810 7 56 3 8.7 8.4 5 9.72 522 9.79 719 10.20281 9.92 803 55 4 11.6 11.2 ' 6 9.72 542 20 9.79 747 28 10.20253 9.92795 8 54 5 14.5 14.0 7 9.72 562 20 9.79 776 29 10.20 224 9.92787 8 53 6 17.4 16.8 8 9.72 582 20 9.79 804 28 10.20 196 9.92779 8 52 7 20.3 19.6 9 9.72 602 20 9.79 832 28 10.20 168 9.92771 8 51 8 23.2 22.4 10 9.72 622 20 9.79 860 28 10.20 140 9.92 763 8 50 9 26.1 25.2 11 9.72 643 21 9.79 888 28 10.20112 9.92755 8 49 12 9.72 663 20 9.79 916 28 10.20 084 9.92 747 8 48 OT 01 13 9.72 683 20 9.79 944 28 10.20056 9.92739 8 47 27 21 14 9.72 703 20 9.79 972 28 10.20 028 9.92731 8 46 2 5.4 4.2 15 9.72 723 20 9.80 000 28 10.20 000 9.92 723 8 45 3 8.1 6.3 16 9.72 743 20 9.80 028 28 10.19972 9.92715 8 44 4 10.8 8.4 17 9.72 763 20 9.80 056 28 10.19944 9.92707 8 43 5 13.5 10.5 18 9.72 783 20 9.80 084 28 10.19916 9.92 699 8 42 6 16.2 12.6 19 9.72 803 20 9.80 112 28 10.19888 9.92691 8 41 7 18.9 14.7 20 28 8 8 21.6 16.8 20 9.72 823 9.80 140 10.19 860 9.92 683 40 9 24.3 18.9 21 9.72 843 20 9.80 168 2o 10.19832 9.92675 8 39 22 9.72 863 20 9.80 195 27 10.19 805 9.92 667 8 38 23 9.72 883 20 9.80 223 28 10.19777 9.92 659 8 37 20 19 24 9.72 902 19 20 9.80 251 28 28 10.19749 9.92651 8 8 36 2 4.0 3.8 25 9.72 922 9.80 279 10.19721 9.92 643 35 3 6.0 5.7 26 9.72 942 20 9.80 307 28 10.19693 9.92 635 8 34 4 8.0 7.6 27 9.72 962 20 9.80 335 28 10.19665 9.92627 8 33 5 10.0 9.5 28 9.72 982 20 9.80 363 28 OQ 10.19637 9.92 619 8 32 6 12.0 11.4 29 9.73 002 20 20 9.80 391 ma 28 10.19609 9.92611 8 8 31 7 14.0 13.3 30 9.73 022 9.80 419 10.19 581 9.92 603 30 8 16.0 15.2 31 9.73 041 19 9.80 447 28 10.19553 9.92 595 8 29 9 18.0 17.1 32 9.73 061 20 9.80 474 27 10.19526 9.92 587 8 28 33 9.73 081 20 9.80 502 28 10.19498 9.92579 8 27 34 9.73 101 20 9.80 530 28 10.19470 9.92571 8 26 9 a Y 35 9.73 121 20 9.80 558 28 10.19442 9.92563 8 25 2 1.8 1.6 1.4 36 9.73 140 19 9.80 586 28 10.19414 9.92 555 8 24 3 2.7 -2.4 2.1 37 9.73 160 20 9.80 614 28 10.19386 9.92 546 9 23 4 3.6 3.2 2.8 38 9.73 180 20 9.80 642 28 10.19358 9.92538 8 22 5 4.5 4.0 3.5 39 9.73 200 20 9.80 669 27 10.19331 9.92 530 8 21 6 5.4 4.8 4.2 40 9.73 219 19 9.80 697 28 10.19303 9.92 522 8 20 7 6.3 5.6 4.9 7O A A Ci A 41 9.73 239 20 9.80 725 28 10.19275 9.92514 8 19 tA O.T; O.O 81 79 A Q 42 9.73 259 20 9.80 753 28 10.19247 9.92506 8 18 .1 { mm O.O 43 9.73 278 19 9.80 781 28 10.19219 9.92498 8 17 44 45 9.73 298 9.73 318 20 20 9.80 808 9.80 836 27 28 10.19 192 10.19 164 9.92490 9.92482 8 8 16 15 From the top: 46 9.73 337 19 9.80 864 28 10.19 136 9.92473 9 14 For32+or212 0+ , 47 48 49 9.73 357 9.73 377 9.73 396 20 20 19 9.80 892 9.80919 9.80 947 28 27 28 10.19 108 10.19081 10.19053 9.92 465 9.92457 9.92449 8 8 S 13 12 11 read as printed; for 122+ or 302+, read 50 9.73 416 20 9.80 975 28 10.19025 9.92441 8 10 co-function. 51 9.73 435 19 9.81 003 28 10.18997 9.92433 8 9 52 53 9.73 455 9.73 474 20 19 9.81 030 9.81 058 27 28 10.18970 10.18942 9.92425 9.92416 8 g 8 7 From the bottom: 54 55 56 57 ^73494^ 9!73~513 9.73 533 9.73 552 20 19 20 19 9.81 086 9.81 113 9.81 141 9.81 169 28 27 28 28 10.18914 10.18887 10.18859 10.18831 9.92408 9.92400 9.92392 9.92 384 8 8 8 S 6 5 4 3 For 57+ or 237+, read as printed ; for 147+ or 327+, read 58 9.73 572 20 9.81 196 27 10.18804 9.92 376 8 2 co-function. 59 9.73 591 19 20 9.81 224 28 28 10.18776 9.92367 8 1 60 9.73611 9.81 252 10.18748 9.92 359 LCos d LCtn c d L Tan L Sin d ' Prop. Pts. 57 Logarithms of Trigonometric Functions Ill] 33 Logarithms of Trigonometric Functions 79 ' LSin d LTan cd LCtn LCos d Prop. Pts. 9.73611 9.81 252 10.18748 9.92 359 60 1 9.73 630 19 9.81 279 27 10.18721 9.92351 8 59 2 9.73 650 20 9.81 307 28 10.18693 9.92 343 8 58 28 27 3 9.73 669 19 9.81 335 28 10.18665 9.92335 S 57 2 5.6 5.4 4 9.73 689 20 19 9.81 362 27 28 10.18638 9.92 326 9 g 56 3 8.4 8.1 5 9.73 708 9.81 390 10.18610 9.92318 55 4 11.2 10.8 6 9.73 727 19 9.81 418 28 10.18582 9.92310 S 54 5 14.0 13.5 7 9.73 747 20 9.81 445 27 10.18555 9.92 302 S 53 6 16.8 16.2 8 9.73 766 19 9.81 473 28 10.18527 9.92 293 9 52 7 19.6 18.9 9 9.73 785 19 9.81 500 27 10.18500 9.92 285 S 51 8 22.4 21.6 10 9.73 805 20 9.81 528 28 10.18472 9.92 277 S 50 9 25.2 24.3 11 9.73 824 19 9.81 556 28 10.18444 9.92 269 8 49 12 9.73 843 19 9.81 583 27 10.18417 9.92260 9 48 OA *n 13 9.73 863 20 9.81611 28 10.18389 9.92252 8 47 20 * 14 9.73 882 19 9.81 638 27 10.18362 9.92 244 S 46 2 4.0 3.8 15 9.73 901 19 9.81 666 28 10.18334 9.92 235 9 45 3 6.0 5.7 16 9.73 921 20 9.81 693 27 10.18307 9.92 227 S 44 4 8.0 7.6 17 9.73 940 19 9.81 721 28 10.18279 9.92219 S 43 5 10.0 9.5 18 9.73 959 19 9.81 748 27 10.18252 9.92211 S 42 6 12.0 11.4 19 9.73 978 19 9.81 776 28 10.18224 9.92 202 9 g 41 7 8 14.0 16.0 13.3 20 9.73 997 9.81 803 10.18 197 9.92 194 40 9 18.0 17^1 21 9.74 017 20 9.81 831 28 10.18169 9.92 186 8 39 22 9.74 036 19 9.81 858 27 10.18 142 9.92 177 9 38 23 9.74 055 19 9.81 886 28 10.18114 9.92 169 8 37 18 9 24 9.74 074 19 19 9.81 913 27 28 10.18087 9.92 161 8 9 36 2 3.6 1.8 25 9.74 093 9.81 941 10.18059 9.92 152 35 3 5.4 2.7 26 9.74 113 20 9.81 968 27 10.18032 9.92 144 8 34 4 7.2 3.6 27 9.74 132 19 9.81 996 28 10.18004 9.92 136 8 33 5 9.0 4.5 28 9.74 151 19 9.82 023 27 10.17977 9.92 127 9 32 6 10.8 5.4 29 9.74 170 19 19 9.82 051 28 27 10.17949 9.92119 S g 31 7 12.6 6.3 30 9.74 189 9.82 078 10.17922 9.92111 30 8 14.4 7.2 31 9.74 208 19 9.82 106 28 10.17 894 9.92 102 9 29 9 16.2 8.1 32 9.74 227 19 9.S2 133 27 10.17867 9.92 094 8 28 33 9.74 246 19 9.82 161 28 10.17839 9.92 086 8 27 34 9.74 265 19 9.82 188 27 10.17812 9.92 077 9 26 8 35 9.74 284 19 9.82 215 27 10.17785 9.92069 8 25 2 1.6 36 9.74 303 19 9.82 243 28 10.17757 9.92 060 9 24 3 2.4 37 9.74 322 19 9.82270 27 10.17730 9.92052 S 23 4 3.2 38 9.74 341 19 9.82 298 28 10.17702 9.92 044 8 22 6 4.0 39 9.74 360 19 9.82 325 27 10.17675 9.92035 9 21 6 4.8 40 9.74 379 19 9.82 352 27 10.17 648 9.92 027 S 20 7 5.6 8 A A 41 9.74 398 19 9.82 380 28 10.17620 9.92018 9 ia D.4 9*7 O 42 9.74 417 19 9.82 407 27 10.17593 9.92010 S 18 7.4 43 9.74 436 19 9.82 435 28 10.17565 9.92002 8 17 44 45 9.74 455 9.74 474 19 19 9.82 462 9.82 489 27 27 10.17538 10.17511 9.91 993 9.91 985 9 8 16 15 From the top: 46 9.74 493 19 9.82517 28 10.17483 9.91976 9 14 For33 0+ or213 8+ , 47 48 49 9.74512 9.74 531 9.74 549 19 19 18 9.82 544 9.82 571 9.82 599 27 27 28 10.17456 10.17429 10.17401 9.91 968 9.91 959 9.91951 8 9 8 13 12 11 read as printed; for 123 0+ or303- t -,read 50 9.74 568 19 9.82 626 27 10.17374 9.91 942 9 10 co-function. 51 9.74 587 19 9.82 653 27 10.17 347 9.91934 8 9 52 53 9.74 606 9.74 625 19 19 9.82 681 9.82 708 28 27 10.17319 10.17292 9.91925 9.91917 9 S 8 7 From the bottom: 54 9.74 644 19 18 9.82 735 27 27 10.17265 9.91908 9 S 6 For56- ( -or236 0+ , 55 56 57 9.74 662 9.74 681 9.74 700 19 19 9.82762 9.82 790 9.82 817 28 27 10.17238 10.17210 10.17183 9.91 900 9.91 891 9.91 883 9 8 5 4 3 read as printed ; for 146+ or 326+ read 58 9.74719 19 9.82 844 27 10.17 156 9.91 874 9 2 co-function. 59 9.74 737 18 9.82 871 27 10.17 129 9.91866 8 1 60 9.74 756 19 9.82 89S 28 10.17101 9.91 857 9 LCos d L Ctn cd LTan L Sin d Prop. Pts. 56 Logarithms of Trigonometric Functions 80 34 Logarithms of Trigonometric Functions [in ' LSin d LTan cd LCtn L Cos d Prop. Pts. 9.74 756 9.82 899 10.17101 9.91 857 60 1 9.74 775 19 9.82 926 27 10.17074 9.91 849 8 59 2 9.74 794 19 9.82 953 27 10.17047 9.91840 9 58 28 27 3 9.74 812 18 9.82 980 27 10.17020 9.91 832 8 57 5t* 4 9.74 831 19 19 9.83 008 28 27 10.16992 9.91 823 9 56 3 .D 8.4 8.1 5 9.74 850 9.83 035 10.16965 9.91815 55 4 11.2 10.8 6 9.74 868 18 9.83 062 27 10.16938 9.91 806 9 54 5 14.0 13.5 7 9.74 887 19 9.83 089 27 10.16911 9.91 798 8 53 6 16.8 16.2 8 9.74 906 19 9.83 117 28 10.16883 9.91 789 9 52 7 19.6 18.9 9 9.74 924 18 9.83 144 27 10.16856 9.91 781 8 51 8 22.4 21.6 10 9.74 943 19 9.83 171 27 10.16829 9.91 772 9 50 9 25.2 24.3 11 9.74 961 18 9.83 198 27 10.16802 9.91763 9 49 12 9.74 980 19 9.83 225 27 10.16775 9.91 755 8 48 13 9.74 999 19 9.83 252 27 10.16748 9.91 746 9 47 20 19 14 9.75 017 18 9.83 280 28 10.16720 9.91 738 8 46 2 5.2 3.8 15 9.75 036 19 9.83 307 27 10.16693 9.91 729 9 45 3 7.8 5.7 16 9.75 054 18 9.83 334 27 10.16666 9.91720 9 44 4 10.4 7.6 17 9.75 073 19 9.83 361 27 10.16639 9.91712 8 43 5 13.0 9.5 18 9.75 091 18 9.83 388 27 10.16612 9.91 703 9 42 6 15.6 11.4 19 9.75 110 19 9.83 415 27 10.16585 9.91 695 8 41 7 18.2 13.3 20 21 9.75 128 9.75 147 19 9.83 442 9.83 470 28 10.16558 10.16530 9.91 686 9.91 677 9 9 40 39 8 9 20.8 23.4 15.2 17.1 22 9.75 165 18 9.83 497 27 10.16503 9.91 669 8 38 23 9.75 184 19 9.83 524 27 10.16476 9.91660 9 37 18 q 24 9.75 202 18 19 9.83 551 27 27 10.16449 9.91651 9 8 36 2 3.6 V 1.8 25 9.75 221 1 Q 9.83 578 10.16422 9.91 643 35 3 5.4 2.7 26 9.75 239 18 9.83 605 27 10.16395 9.91634 9 34 4 7.2 3.6 27 9.75 258 19 9.83 632 27 10.16368 9.91 625 9 33 5 9.0 4.5 28 9.75 276 18 1 Q 9.83 659 27 10.16341 9.91617 8 32 6 iols 5 4 29 9.75 294 lo 19 9.83 686 27 27 10.16314 9.91608 9 g 31 7 12.6 6.3 30 9.75 313 9.83 713 10.16287 9.91 599 30 8 14.4 7.2 31 9.75 331 18 9.83 740 27 10.16260 9.91591 8 29 9 16.2 8.1 32 9.75 350 19 9.83 768 28 10.16232 9.91582 9 28 33 9.75 368 18 9.83 795 27 10.16205 9.91573 9 27 34 9.75 386 18 19 9.83 822 27 27 10.16 178 9.91565 8 9 26 8 35 9.75 405 9.83 849 10.16151 9.91656 25 2 1.6 30 9.75 423 18 9.83 876 27 10.16124 9.91 547 9 24 3 2.4 37 9.75 441 18 9.83 903 27 10.16097 9.91538 9 23 4 3.2 38 9.75 459 18 9.83 930 27 10.16070 9.91530 8 22 5 4.0 39 9.75 478 19 9.83 957 27 10.16043 9.91521 9 21 6 4.8 40 9.75 496 18 9.83 984 27 10.16016 9.91512 9 20 7 5.6 41 9.75514 18 9.84011 27 10.15989 9.91504 8 19 8 6.4 42 9.75 533 19 9.84 038 27 10.15962 9.91495 9 18 9 7.2 43 9.75 551 18 9.84 065 27 10.15935 9.91486 9 17 44 9.75 569 18 9.84 092 27 10.15908 9.91477 9 16 45 9.75 587 18 9.84 119 27 10.15881 9.91 469 8 15 From the top: 40 9.75 605 18 9.84 146 27 10.15854 9.91460 9 14 For34- ( -or214 0+ , 47 48 49 9.75 624 9.75 642 9.75 660 19 18 18 9.84 173 9.84 200 9.84 227 27 27 27 10.15827 10.15800 10.15773 9.91451 9.91442 9.91433 9 9 9 13 12 11 read as printed ; for 124+ or 304+, read 50 9.75 678 18 9.84 254 27 10.15746 9.91425 8 10 co-function. 51 9.75 696 18 9.84 280 26 10.15720 9.91416 9 9 52 9.75 714 18 9.84 307 27 10.15693 9.91407 9 8 53 9.75 733 19 9.84 334 27 10.15666 9.91398 9 7 From the bottom: 54 9.75 751 18 18 9.84 361 27 27 10.15639 9.91389 9 8 6 For 55+ or 235+, 55 50 57 9.75 769 9.75 787 9.75 805 18 18 9.84 388 9.84415 9.84 442 27 27 10.15612 10.15585 10.15558 9.91 381 9.91372 9.91363 9 9 5 4 3 read as printed ; for 145 0+ or325- f ,read 58 9.75 823 18 9.84 469 27 10.15531 9.91354 9 2 co-function. 59 9.75 841 18 9.84 496 27 10.15504 9.91 345 9 1 60 9.75 859 18 9.84 523 27 10.15477 9 91 336 J LCos d LCtn cd LTan LSin d ' Prop. Pts. 55 Logarithms of Trigonometric Functions Ill] 35 Logarithms of Trigonometric Functions 81 / LSin d LTan cd L Ctn LCos d Prop. Pts. 9.75 859 9.84 523 10.15477 9.91 336 60 1 9.75877 18 9.84550 27 10.15450 9.91328 s 59 2 9.75 895 18 9.84576 26 10.15424 9.91319 9 58 27 26 3 9.75913 18 9.84 603 27 10.15397 9.91310 9 57 2 5.4 5.2 4 9.75931 18 18 9.84630 27 27 10.15370 9.91301 9 9 56 3 8.1 7.8 5 9.75 949 9.84 657 10.15 343 9.91292 55 4 10.8 10.4 6 9.75967 18 9.84684 27 10.15316 9.91283 9 54 5 13.5 13.0 7 9.75 985 18 9.84711 27 10.15289 9.91274 9 53 6 16.2 15.6 8 9.76 003 IS 9.84738 27 10.15262 9.91266 8 52 7 18.9 18.2 9 9.76021 18 9.84764 26 10.15236 9.91 257 9 51 8 21.6 20.8 10 9.76 039 18 9.84791 27 10.15 209 9.91 248 9 50 9 24.3 23.4 11 9.76057 18 9.84 8ia 27 10.15 182 9.91 239 9 49 12 9.76075 18 9.S4S45 27 10.15155 9.91230 9 48 f O 1 T 13 9.76093 18 9.84 87* < i 27 10.15128 9.91221 9 47 18 17 14 9.76111 18 9.84 899 27 10.15 101 9.91212 9 46 2 3.6 3.4 15 9.76 129 18 9.84 925 26 10.15 075 9.91 203 9 45 3 5.4 5.1 16 9.76 146 17 9.84 952 27 10.15 048 9.91 194 9 44 4 7.2 6.8 17 9.76 164 18 9.84979 27 10.15021 9.91 185 9 43 5 9.0 8.5 18 9.76 182 18 9.85 006 27 10.14994 9.91 176 9 42 6 10.8 10.2 19 9.76200 18 9.85 033 27 10.14967 9.91 167 9 41 7 12.6 11.9 18 26 9 3 14.4 13.6 20 9.76218 9.85 059 O*7 10.14941 9.91 158 40 9 16.2 15.3 21 9.76 236 18 9.85 086 1 10.14914 9.91 149 9 39 22 9.76253 17 9.85 113 27 10.14887 9.91 141 S 38 23 9.76271 18 9.85 140 27 10.14860 9.91 132 9 37 10 9 24 9.76289 18 18 9.85 166 26 27 10.14834 9.91 123 9 9 36 2 2.0 1.8 25 9.76307 9.85 193 10.14807 9.91 114 35 3 3.0 2.7 26 9.76324 17 9.85 220 27 10.14780 9.91 105 9 34 4 4.0 3.6 27 9.76342 18 f Q 9.85 247 27 OA 10.14753 9.91 096 9 33 5 5.0 4.5 28 9.76360 18 9.85 273 Jo 10.14727 9.91 087 32 6 6.0 5.4 29 9.76378 18 17 9.85 300 27 27 10.14700 9.91078 9 9 31 7 7.0 6.3 30 9.76395 9.85 327 10.14673 9.91 069 30 8 8.0 7.2 31 9.76413 18 9.85 354 27 10.14646 9.91 060 9 29 9 9.0 8.1 32 9.76431 18 9.85 380 26 10.14620 9.91 051 9 28 33 9.76448 17 9.85407 27 10.14593 9.91 042 9 27 34 9.76466 18 9.85 434 27 10.14566 9.91033 9 26 8 35 9.76484 18 9.85 460 26 10.14540 9.91 023 10 25 2 1.6 36 9.76501 17 9.85 487 27 10.14513 9.91014 9 24 3 2.4 37 9.76519 18 9.85514 27 10.14486 9.91005 9 23 4 3.2 38 9.76537 IS 9.85 540 26 10.14460 9.90996 9 22 5 4.0 39 9.76554 17 9.85 567 27 10.14433 9.90 987 9 21 6 4.8 40 9.76572 18 9.85 594 27 10.14406 9.90978 9 20 7 5.6 41 9.76590 18 9.85 620 26 10.14380 9.90969 9 19 8 6.4 42 9.76 607 17 9.85 647 27 10.14353 9.90960 9 18 9 7.2 43 9.76 625 IS 9.85 674 27 10.14326 9.90951 9 17 44 9.76 642 17 9.85 700 26 10.14300 9.90 942 9 16 45 9.76 660 18 9.85 727 27 10.14273 9.90 933 9 15 From the top: 46 9.76 677 17 9.85 754 27 10.14 246 9.90 924 9 14 For 35+ or 215+, 47 48 49 9.76 695 9.76712 9.76730 18 17 18 9.85 780 9.85 807 9.85 834 26 27 27 10.14220 10.14193 10.14166 9.90915 9.90906 9.90 896 9 10 13 12 11 read as printed ; for 125 0+ or305 0+ ,read 50 9.76 747 17 9.85 860 26 10.14140 9.90887 9 10 co-function. 51 9.76 765 18 9.85 887 27 10.14113 9.90 878 9 9 52 9.76782 17 9.85913 26 10.14087 9.90869 9 8 53 9.76 800 18 9.85 940 27 10.14060 9.90 860 9 7 From the bottom: 54 9.76817 17 IS 9.85 967 27 26 10.14033 9.90851 9 9 6 For 54+ or 234+, 55 56 57 9.76 835 9.76 852 9.76 870 17 18 9.85 993 9.86020 9.86046 27 26 10.14007 10.13980 10.13954 9.90842 9.90 832 9.90 823 10 9 5 4 3 read as printed ; for 144+ or 324+ read 58 9.76 887 17 9.86 073 27 10.13 927 9.90814 9 2 co-function. 59 9.76 904 17 9.86 100 27 10.13900 9.90 805 9 T 60 9.76 922 IS 9.86126 26 10.13 874 9.90 796 9 LCos d LCtn cd L Tan LSin d / Prop. Pts. 54 Logarithms of Trigonometric Functions 82 36 Logarithms of Trigonometric Functions [III LSin d LTan cd LCtn L Cos d Prop. Pts. 9.76 922 9.86 126 10.13874 9.90796 60 1 9.76 939 17 9.86 153 27 10.13847 9.90787 9 59 2 9.76957 18 9.86 179 26 10.13821 9.90777 10 58 27 26 3 9.76974 17 9.86206 27 10.13794 9.90768 9 57 2 5 4 5.2 4 9.76991 17 18 9.86232 26 27 10.13768 9.90759 9 9 56 3 8.1 7.8 5 9.77009 9.86259 10.13741 9.90750 55 4 10.8 10.4 6 9.77026 17 9.86285 26 10.13715 9.90741 9 54 5 13.5 13.0 7 9.77043 17 9.86312 27 10.13688 9.90731 10 53 6 16.2 15.6 8 9.77061 18 9.86338 26 10.13662 9.90722 9 52 7 18.9 18.2 9 9.77078 17 9.86365 27 10.13635 9.90713 9 51 8 21.6 20.8 10 9.77095 17 9.86392 27 10.13608 9.90704 9 50 9 24.3 23.4 11 9.77112 17 9.86418 26 10.13582 9.90694 10 49 12 9.77 130 18 9.86445 27 10.13 555 9.90685 9 48 13 9.77 147 17 9.86471 26 10.13529 9.90676 9 47 18 11 14 9.77 164 17 9.86498 27 10.13502 9.90 667 9 46 2 3.6 3.4 15 9.77 181 17 9.86524 26 10.13476 9.90 657 10 45 3 5.4 5.1 16 9.77 199 18 9.86551 27 10.13449 9.90648 9 44 4 7.2 6.8 17 9.77216 17 9.86577 26 10.13423 9.90639 9 43 5 9.0 8.5 18 9.77233 17 9.86603 26 10.13397 9.90630 9 42 6 10.8 10.2 19 9.77250 17 9.86630 27 10.13370 9.90620 10 41 7 12.6 11.9 18 26 9 8 14.4 13.6 20 9.77268 9.86 656 10.13344 9.90611 40 g 16.2 15.3 21 9.77 285 17 9.86 683 27 10.13317 9.90 602 9 39 22 9.77302 17 9.86709 26 10.13291 9.90592 10 38 23 9.77319 17 9.86736 27 10.13264 9.90583 9 37 16 10 24 9.77336 17 17 9.86762 26 27 10.13238 9.90574 9 9 36 2 3.2 2.0 25 9.77353 9.86789 10.13211 9.90565 35 3 4.8 3.0 26 9.77370 17 9.86815 26 10.13 185 9.90555 10 34 4 6.4 4.0 27 9.77387 17 9.86842 27 10.13 158 9.90546 9 33 5 8.0 5.0 28 9.77405 18 9.86868 26 10.13132 9.90537 9 32 6 9.6 6.0 29 9.77422 17 17 9.86894 26 27 10.13 106 9.90527 10 9 31 7 11.2 7.0 30 9.77439 9.86921 10.13 079 9.90518 30 8 12.8 8.0 31 9.77456 17 9.86 947 26 10.13053 9.90509 9 29 9 14.4 9.0 32 9.77473 17 9.86 974 27 10.13026 9.90499 10 28 33 9.77490 17 9.87000 26 10.13000 9.90490 9 27 34 9.77 507 17 9.87027 27 10.12973 9.90480 10 26 9 35 9.77 524 17 9.87053 26 10.12947 9.90471 9 25 2 1.8 36 9.77541 17 9.87079 26 10.12921 9.90462 9 24 3 2.7 37 9.77558 17 9.87 106 27 10.12894 9.90452 10 23 4 3.6 38 9.77575 17 9.87 132 26 10.12868 9.90443 9 22 5 4.5 39 9.77592 17 9.87 158 26 10.12 842 9.90434 9 21 6 5.4 40 9.77(509 17 9.87 185 27 10.12815 9.90424 10 20 7 6.3 41 9.77 626 17 9.87211 26 10.12789 9.90415 9 19 8 7.2 42 9.77643 17 9.87238 27 10.12762 9.90405 10 18 9 8.1 43 9.77 660 17 9.87264 26 10.12736 9.90396 9 17 44 9.77677 17 9.87290 26 10.12710 9.90386 10 16 45 9.77694 17 9.87317 27 10.12 683 9.90 377 9 15 From the top: 46 9.77711 17 9.87343 26 10.12657 9.90368 9 14 For36 0+ or216+, 47 48 49 9.77728 9.77744 9.77761 17 16 17 9.87369 9.87396 9.87422 26 27 26 10.12631 10.12604 10.12578 9.90358 9.90 349 9.90339 10 9 10 13 12 11 read as printed; for 126+ or 306+ read 50 9.77778 17 9.87448 26 10.12552 9.90330 9 10 co-function. 51 9.77 795 17 9.87475 27 10.12525 9.90320 10 9 52 53 9.77812 9.77 829 17 17 9.87501 9.87527 26 26 10.12499 10.12473 9.90311 9.90301 9 10 8 7 From the bottom: 54 9.77 846 17 16 9.87 554 27 26 10.12446 9.90292 9 10 6 For 53+ or 233+, 55 56 57 9.77 862 9.77 879 9.77 896 17 17 9.87580 9.87606 9.87 633 26 27 10.12420 10.12394 10.12367 9.90282 9.90273 9.90 263 9 10 5 4 3 read as printed ; for 143+ or 323+, read 58 9.77913 17 9.87659 26 10.12341 9.90 254 9 2 co-function. 59 9.77930 17 9.87685 26 10.12315 9.90 244 10 1 60 9.77946 16 9.87711 26 10.12289 9.90 235 9 LCos d LCtn cd LTan LSin d / Prop. Pts. 53 Logarithms of Trigonometric Functions Ill] 37 Logarithms of Trigonometric Functions 83 : LSin d L Tan cd LCtn LCos d Prop Pts. 9.77946 9.87711 10.12289 9.90 235 60 1 9.77 963 17 9.87738 27 10.12262 9.90 225 10 59 2 9.77 980 17 9.87 764 26 10.12236 9.90216 9 58 3 9.77997 17 9.87790 26 10.12210 9.90206 10 57 4 9.78013 16 17 9.87817 27 26 10.12 183 9.90 197 9 10 56 5 9.78 030 9.87 843 10.12 157 9.90 187 55 27 26 6 9.78047 17 9.87 869 26 OA 10.12131 9.90 178 9 54 2 5.4 5.2 7 9.78 063 16 9.87 895 zo 10.12 105 9.90 168 10 53 8'i 7 S. 8 9 9.78 080 9.78097 17 17 16 9.87 922 9.87 948 27 26 26 10.12078 10.12052 9.90 159 9.90 149 9 10 10 52 51 o 4 5 .1 10.8 13.5 1 .0 10.4 13.0 10 9.78113 *.87 974 10.12026 9.90 139 50 6 16.2 15.6 11 9.78130 17 9.88000 26 10.12000 9.90 130 9 49 7 18.9 18.2 12 9.78 147 17 9.88027 27 10.11973 9.90 120 10 48 8 21.6 20.8 13 9.78 163 16 9.88053 26 10.11 947 9.90111 9 47 9 24.3 23.4 14 9.78 180 17 9.88079 26 10.11921 9.90 101 10 46 15 9.78 197 17 9.88 105 26 10.11 895 9.90 091 10 45 16 9.78213 16 9.88 131 26 10.11869 9.90082 9 44 17 1ft 17 9.78230 17 9.88 158 27 10.11842 9.90072 10 43 Jtl J.O 18 9.78246 16 9.88 184 26 10.11816 9.90 063 9 43 2 3.4 3.2 19 9.78263 17 1 7 9.88210 26 10.11790 9.90053 10 1 C\ 41 3 5.1 A Q 4.8 /; j 20 9.78 280 it 9.88236 10.11764 9.90043 iv 40 5 O.8 8.5 O.4 Q O 21 9.78296 16 9.88262 26 10.11738 9.90 034 9 39 21 9.80213 16 9.91379 26 10.08621 9.88 834 10 39 6 ti i *i> q n 22 23 24 9.80228 9.80244 9.80259 15 16 15 15 9.91 4Q4 9.91430 9.91456 25 26 26 26 10.08596 10.08570 10.08 544 9.88 824 9.88813 9.88803 10 11 10 10 38 37 36 7 8 9 j.\j 11.2 12.8 14.4 7 VlOn Fi 3 31 \re \ 10 Fl \100Fl 1/Fl 1.50 2.2500 1.22474 3.87298 3.37500 1.14471 2.46621 5.31329 .606667 1.51 1.52 1.53 2.2801 2.3104 2.3409 1.22882 1.23288 1.23693 3.88587 3.89872 3.91152 3.44295 3.51181 3.58158 1.14725 1.14978 1.15230 2.47168 2.47712 2.48255 5.32507 5.33680 5.34848 .662252 .657895 .653595 1.54 1.55 1.56 2.3716 2.4025 2.4336 1.24097 1.24499 1.24900 3.92428 3.93700 3.94968 3.65226 3.72388 3.79642 1.15480 1.15729 1.15978 2.48794 2.49332 2.49867 5.36011 5.37169 5.38321 .649351 .645161 .641026 1.57 1.58 1.59 2.4649 2.4964 2.5281 1.25300 1.25698 1.26095 3.96232 3.97492 3.98748 3.86989 3.94431 4.01968 1.16225 1.16471 1.16717 2.50399 2.50930 2.51458 5.39469 5.40612 5.41750 .636943 .632911 .628931 1.60 2.5600 1.26491 4.00000 4.09600 1.16961 2.51984 5.42884 .625000 1.61 1.62 1.63 2.5921 2.6244 2.6569 1.26886 1.27279 1-27671 4.01248 4.02492 4.03733 4.17328 4.25153 4.33075 1.17204 1.17446 1.17687 2.52508 2.53030 2.53549 5.44012 5.45136 5.46256 .621118 .617284 .613497 1.64 1.65 1.66 1.67 1.68 1.69 2.3896 2.7225 2.7556 2^889 2.8224 2.8561 1.28062 1.28452 1.28841 1.29228 1.29615 1.30000 4.04969 4.06202 4.07431 4.08656 4.09878 4.11096 4.41094 4.49212 4.57430 4.65746 4.74163 4.82681 1.17927 1.18167 1.18406 1.18642 1.18878 1.19114 2.54067 2.54582 2.55095 2.55607 2.56116 2.56623 5.47370 5.48481 5.49586 5.50688 5.51785 5.52877 .609756 .606061 .602410 .598802 .595238 .591716 1.70 2.8900 1.30384 4.12311 4.91300 1.19348 2.57128 5.53966 .588235 1.71 1.72 1.73 2.9241 2.9584 2.9929 1.30767 1.31149 1.31529 4.13521 4.14729 4.15933 5.00021 5.08845 5.17772 1.19582 1.19815 1.20046 2.57631 2.58133 2.58632 5.55050 5.56130 5.57205 .584795 581395 .578035 1.74 1.75 1.76 3.0276 3.0625 3.0976 1.31909 1.32288 1.32665 4.17133 4.18330 4.19524 5.26802 5.35938 5.45178 1.20277 1.20507 1.20736 2.59129 2.59625 2.60118 5.58277 5.59344 5.60408 .574713 .571429 .568182 1.77 1.78 1.79 3.1329 3.1684 3.2041 1.33041 1.33417 1.33791 4.20714 4.21900 4.23084 5.54523 5.63975 5.73534 1.20964 1.21192 1.21418 2.60610 2.61100 2.61588 5.61467 5.62523 5.63574 .564972 .561798 .558659 1.80 3.2400 1.34164 4.24264 5.83200 1.21644 2.62074 5.64622 .555556 1.81 1.82 1.83 3.2761 3.3124 3.3489 1.34536 1.34907 1.35277 4.25441 4.26615 4.27785 5.92974 6.02857 6.12849 1.21869 1.22093 1.22316 2.62559 2.63041 2.63522 5.65665 5.66705 5.67741 .552486 .549451 .546448 1.84 1.85 1.86 3.3856 3.4225 3.4596 1.35647 1.36015 1.36382 4.28952 4.30116 4.31277 6.22950 6.33162 6.43486 1.22539 1.22760 1.22981 2.64001 2.64479 2.64954 5.68773 5.69802 5.70827 .543478 .540541 .537634 1.87 1.88 1.89 3.4969 3.5344 3.5721 1.36748 1.37113 1.37477 4.32435 4.33590 4.34741 6.53920 6.64467 6.75127 1.23201 1.23420 1.23639 2.65428 2.65901 2.66371 5.71848 5.72865 5.73879 .534759 .531915 .529101 1.90 3.6100 1.37840 4.35890 6.85900 1.23856 2.66840 5.74890 .526316 1.91 1.92 1.93 3.6481 3.6864 3.7249 1.38203 1.38564 1.38924 4.37035 4.38178 4.39318 6.96787 7.07789 7.18906 1.24073 1.24289 1.24505 2.67307 2.67773 2.68237 5.75897 5.76900 5.77900 .523560 .520833 .518135 1.94 1.95 1.96 3.7636 3.8025 3.8416 1.39284 1.39642 1.40000 4.40454 4.41588 4.42719 7.30138 7.41488 7.52954 1.24719 1.24933 1.25146 2.68700 2.69161 2.69620 5.78896 5.79889 5.80879 .515464 .512821 .510204 1.97 1.98 1.99 3.8809 3.9204 3.9601 1.40357 1.40712 1.41067 4.43847 4.44972 4.46094 7.64537 7.76239 7.88060 1.25359 1.25571 1.25782 2.70078 2.70534 2.70989 5.81865 5.82848 5.83827 .507614 .505051 .502513 2.00 4.0000 1.41421 4.47214 8.00000 1.25992 2.71442 5.84804 .500000 n. n 2 vs VlO n Fi 3 3/ \n ^10 n x'lOOn 1/Fl 96 Powers Roots Reciprocals [VI n n 2 V^ VToTI n 3 \ln ^10 n A'100 11 l/n 2.00 4.0000 1.41421 4.47214 8.00000 1.25992 2.71442 5.84804 .500000 2.01 2.02 2.03 4.0401 4.0804 4.1209 1.41774 1.42127 1.42478 4.48330 4.49444 4.50555 8.12060 8.24241 8.36543 1.26202 1.26411 1.26619 2.71893 2.72344 2.72792 5.85777 5.86746 5.87713 .497512 .495050 .492611 2.04 2.05 2.06 4.1616 4.2025 4.2436 1.42829 1.43178 1.43527 4.51664 4.52769 4.53872 8.48966 8.61512 8.74182 1.26827 1.27033 1.27240 2.73239 2.73685 2.74129 5.88677 5.89637 5.90594 .490196 .487805 .485437 2.07 2.08 2.09 4.2849 4.3264 4.3681 1.43875 1.44222 1.44568 4.54973 4.56070 4.57165 8.86974 8.99891 9.12933 1.27445 1.27650 1.27854 2.74572 2.75014 2.75454 5.91548 5.92499 5.93447 .483092 .480769 .478469 2.10 4.4100 1.44914 4.58258 9.26100 1.28058 2.75892 5.94392 .476190 2.11 2.12 2.13 4.4521 4.4944 4.5369 1.45258 1.45602 1.45945 4.59347 4.60435 4.61519 9.39393 9.52813 9.66360 1.28261 1.28463 1.28665 2.76330 2.76766 2.77200 5.95334 5.96273 5.97209 .473934 .471698 .469434 2.14 2.15 2.16 4.5796 4.6225 4.6656 1.46287 1.46629 1.46969 4.62601 4.63681 4.64758 9.80034 9.93838 10.0777 1.28866 1.29066 1.29266 2.77633 2.78065 2.78495 5.98142 5.99073 6.00000 .467290 .465116 .462963 2.17 2.18 2.19 4.7089 4.7524 4.7961 1.47309 1.47648 1.47986 4.65833 4.66905 4.67974 10.2183 10.3602 10.5035 1.29465 1.29664 1.29862 2.78924 2.79352 2.79779 6.00925 6.01846 6.02765 .460829 .458716 .456621 2.20 4.8400 1.48324 4.69042 10.6480 1.30059 2.80204 6.03681 .454545 2.21 2.22 2.23 4.8841 4.9284 4.9729 1.48661 1.48997 1.49332 4.70106 4.71169 4.72229 10.7939 10.9410 11.0896 1.30256 1.30452 1.30648 2.80628 2.81050 2.81472 6.04594 6.05505 6.06413 .452489 .450450 .448430 2.24 2.25 2.26 5.0176 5.0625 5.1076 1.49666 1.50000 1.50333 4.73286 4.74342 4.75395 11.2394 11.3906 11.5432 1.30843 1.31037 1.31231 2.81892 2.82311 2.82728 6.07318 6.08220 6.09120 .446429 .444444 .442478 2.27 2.28 2.29 5.1529 5.1984 5.2441 1.50665 1.50997 1.51327 4.76445 4.77493 4.78539 11.6971 11.8524 12.0090 1.31424 1.31617 1.31809 2.83145 2.83560 2.83974 6.10017 6.10911 6.11803 .440529 .438596 .436681 2.30 5.2900 1.51658 4.79583 12.1670 1.32001 2.84387 6.12693 .434783 2.31 2.32 2.33 5.3361 5.3824 5.4289 1.51987 1.52315 1.52643 4.80625 4.81664 4.82701 12.3264 12.4872 12.6493 1.32192 1.32382 1.32572 2.84798 2.85209 2.85618 6.13579 6.14463 6.15345 .432900 .431034 .429185 2.34 2.35 2.36 5.4756 5.5225 5.5696 1.52971 1.53297 1.53623 4.83735 4.84768 4.85798 12.8129 12.9779 13.1443 1.32761 1.32950 1.33139 2.86026 2.86433 2.86838 6.16224 6.17101 6.17975 .427350 .425532 .423729 2.37 2.38 2.39 5.6169 5.6644 5.7121 1.53948 1.54272 1.54596 4.86826 4.87852 4.88876 13.3121 13.4813 13.6519 1.33326 1.33514 1.33700 2.87243 2.87646 2.88049 6.18846 6.19715 6.20582 .421941 .420168 .418410 2.40 5.7600 1.54919 4.89898 13.8240 1.33887 2.88450 6.21447 .416667 2.41 2.42 2.43 5.8081 5.8564 5.9049 1.55242 1.55563 1.55885 4.90918 4.91935 4.92950 13.9975 14.1725 14.3489 1.34072 1.34257 1.34442 2.88850 2.89249 2.89647 6.22308 6.23168 6.24025 .414938 .413223 .411523 2.44 2.45 2.46 5.9536 6.0025 6.0516 1.56205 1.56525 1.56844 4.93964 4.94975 4.95984 14.5268 14.7061 14.8869 1.34626 1.34810 1.34993 2.90044 2.90439 2.90834 6.24880 6.25732 6.26583 .409836 .408163 .406504 2.47 2.48 2.49 6.1009 6.1504 6.2001 1.57162 1.57480 1.57797 4.96991 4.97996 4.98999 15.0692 15.2530 15.4382 1.35176 1.35358 1.35540 2.91227 2.91620 2.92011 6.27431 6.28276 6.29119 .404858 .403226 .401606 2.50 6.2500 1.58114 5.00000 15.6250 1.35721 2.92402 6.29961 .400000 n n 2 V^ VlOn n 3 fti A/10 n ^100 n l/n VI] Powers Roots Reciprocals 97 n n 2 V^ VlOn n 3 ^ \10 71 \100n l/n 2.50 6.2500 1.58114 5.00000 15.6250 1.35721 2.92402 6.29961 .400000 2.51 2.52 2.53 6.3001 6.3504 6.4009 1.58430 1.58745 1.59060 5.00999 5.01996 5.02991 15.8133 16.0030 16.1943 1.35902 1.36082 1.36262 2.92791 2.93179 2.93567 6.30799 6.31636 6.32470 .398406 .396825 .395257 2.54 2.55 2.56 6.4516 6.5025 6.5536 1.59374 1.59687 1.60000 5.03984 5.04975 5.05964 16.3871 16.5814 16.7772 1.36441 1.36620 1.36798 2.93953 2.94338 2.94723 6.33303 6.34133 6.34960 .393701 .392157 .390625 2.57 2.58 2.59 6.6049 6.6564 6.7081 1.60312 1.60624 1.60935 5.06952 5.07937 5.08920 16.9746 17.1735 17.3740 1.36976 1.37153 1.37330 2.95106 2.95488 2.95869 6.35786 6.36610 6.37431 .389105 .387597 .386100 2.60 6.7600 1.61245 5.09902 17.5760 1.37507 2.96250 6.38250 .384615 2.61 2.62 2.63 6.8121 6.8644 6.9169 1.61555 1.61864 1.62173 5.10882 5.11859 5.12835 17.7796 17.9847 18.1914 1.37683 1.37859 1.38034 2.96629 2.97007 2.97385 6.39068 6.39883 6.40696 .383142 .381679 .380228 2.64 2.65 2.66 6.9696 7.0225 7.0756 1.62481 1.62788 1.63095 5.13809 5.14782 5.15752 18.3997 18.6096 18.8211 1.38208 1.38383 1.38557 2.97761 2.98137 2.98511 6.41507 6.42316 6.43123 .378788 .377358 .375940 2.67 2.68 2.69 7.1289 7.1824 7.2361 1.63401 1.63707 1.64012 5.16720 5.17687 5.18652 19.0342 19.2488 19.4651 1.38730 1.38903 1.39076 2.98885 2.99257 2.99629 6.43928 6.44731 6.45531 .374532 .373134 .371747 2.70 7.2900 1.64317 5.19615 19.6830 1.39248 3.00000 6.46330 .370370 2.71 2.72 2.73 7.3441 7.3984 7.4529 1.64621 1.64924 1.65227 5.20577 5.21536 5.22494 19.9025 20.1236 20.3464 1.39419 1.39591 1.39761 3.00370 3.00739 3.01107 6.47127 6.47922 6.48715 .369004 .367647 .366300 2.74 2.75 2.76 7.5076 7.5625 7.6176 1.65529 1.65831 1.66132 5.23450 5.24404 5.25357 20.5708 20.7969 21.0246 1.39932 1.40102 1.40272 3.01474 3.01841 3.02206 6.49507 6.50296 6.51083 .364964 .363636 .362319 2.77 2.78 2.79 7.6729 7.7284 7.7841 1.66433 1.66733 1.67033 5.26308 5.27257 5.28205 21.2539 21.4850 21.7176 1.40441 1.40610 1.40778 3.02570 3.02934 3.03297 6.51868 6.52652 6.53434 .361011 .359712 .358423 2.80 7.8400 1.67332 5.29150 21.9520 1.40946 3.03659 6.54213 .357143 2.81 2.82 2.83 7.8961 7.9524 8.0089 1.67631 1.67929 1.68226 5.30094 6.31037 5.31977 22.1880 22.4258 22.6652 1.41114 1.41281 1.41448 3.04020 3.04380 3.04740 6.54991 6.55767 6.56541 .355872 .354610 .353357 2.84 2.85 2.86 8.0656 8.1225 8.1796 1.68523 1.68819 1.69115 5.32917 5.33854 5.34790 22.9063 23.1491 23.3937 1.41614 1.41780 1.41946 3.05098 3.05456 3.05813 6.57314 6.58084 6.58853 .352113 .350877 .349650 2.87 2.88 2.89 8.2369 8.2944 8.3521 1.69411 1.69706 1.70000 5.35724 5.36656 5.37587 23.6399 23.8879 24.1376 1.42111 1.42276 1.42440 3.06169 3.06524 3.06878 6.59620 6.60385 6.61149 .348432 .347222 .346021 2.90 8.4100 1.70294 5.38516 24.3890 1.42604 3.07232 6.61911 .344828 2.91 2.92 2.93 8.4681 8.5264 8.5849 1.70587 1.70880 1.71172 5.39444 5.40370 5.41295 24.6422 24.8971 25.1538 1.42768 1.42931 1.43094 3.07584 3.07936 3.08287 6.62671 6.63429 6.64185 .343643 .342466 .341297 2.94 2.95 2.96 8.6436 8.7025 8.7616 1.71464 1.71756 1.72047 5.42218 5.43139 5.44059 25.4122 25.6724 25.9343 1.43257 1.43419 1.43581 3.08638 3.08987 3.09336 6.64940 6.65693 6.66444 .340136 .338983 .337838 2.97 2.98 2.99 8.8209 8.8804 8.9401 1.72337 1.72627 1.72916 5.44977 5.45894 5.46809 26.1981 26.4636 26.7309 1.43743 1.43904 1.44065 3.09684 3.10031 3.10378 6.67194 6.67942 6.68688 .336700 .335570 .334448 3.00 9.0000 1.73205 5.47723 27.0000 1.44225 3.10723 6.69433 .333333 n n 2 V^ Vio n 3 3/ Vn W^ ^lOOT^ l/n 98 Powers Roots Reciprocals [VI 11 n? V^ VlOn n 3 In A/lOn ^100 n 1/n 3.00 9.0000 1.73205 5.47723 27.0000 1.44225 3.10723 6.69433 .333333 3.01 3.02 3.03 9.0601 9.1204 9.1809 1.73494 1.73781 1.74069 5.48635 5.49545 5.50454 27.2709 27.5436 27.8181 1.44385 1.44545 1.44704 3.11068 3.11412 3.11756 6.70176 6.70917 6.71657 .332226 .331126 .330033 3.04 3.05 3.06 9.2416 9.3025 9.3636 1.74356 1.74642 1.74929 5.51362 5.52268 5.53173 28.0945 28.3726 28.6526 1.44863 1.45022 1.45180 3.12098 3.12440 3.12781 6.72395 6.73132 6.73866 .328947 .327869 .326797 3.07 3.08 3.09 9.4249 9.4864 9.5481 1.75214 1.75499 1.75784 5.54076 5.54977 5.55878 28.9344 29.2181 29.5036 1.45338 1.45496 1.45653 3.13121 3.13461 3.13800 6.74600 6.75331 6.76061 .325733 .324675 .323625 3.10 9.6100 1.76068 5.56776 29.7910 1.45810 3.14138 6.76790 .322581 3.11 3.12 3.13 9.6721 9.7344 9.7969 1.76352 1.76635 1.76918 5.57674 5.58570 5.59464 30.0802 30.3713 30.6643 1.45967 1.46123 1.46279 3.14475 3.14812 3.15148 6.77517 6.78242 6.78966 .321543 .320513 .319489 3.14 3.15 3.16 9.8596 9.9225 9.9856 1.77200 1.77482 1.77764 5.60357 5.61249 5.62139 30.9591 31.2559 31.6545 1.46434 1.46590 1.46745 3.15483 3.15818 3.16152 6.79688 6.80409 6.81128 .318471 .317460 .316456 3.17 3.18 3.19 10.0489 10.1124 10.1761 1.78045 1.78326 1.78606 5.63028 5.63915 5.64801 31.8550 32.1574 32.4618 1.46899 1.47054 1.47208 3.16485 3.16817 3.17149 6.81846 6.82562 6.83277 .315457 .314465 .313480 3.20 10.2400 1.78885 5.65685 32.7680 1.47361 3.17480 6.83990 .312500 3.21 3.22 3.23 10.3041 10.3684 10.4329 1.79165 1.79444 1.79722 5.66569 5.67450 5.68331 33.0762 33.3862 33.6983 1.47515 1.47668 1.47820 3.17811 3.18140 3.18469 6.84702 6.85412 6.86121 .311526 .310559 .309598 3.24 3.25 3.26 10.4976 10.5625 10.6276 1.80000 1.80278 1.80555 5.69210 5.70088 5.70964 34.0122 34.3281 34.6460 1.47973 1.48125 1.48277 3.18798 3.19125 3.19452 6.86829 6.87534 6.88239 .308642 .307692 .306748 3.27 3.28 3.29 10.6929 10.7584 10.8241 1.80831 1.81108 1.81384 5.71839 5.72713 5.73585 34.9658 35.2876 35.6113 1.48428 1.48579 1.48730 3.19778 3.20104 3.20429 6.88942 6.89643 6.90344 .305810 .304878 .303951 3.30 10.8900 1.81659 5.74456 35.9370 1.48881 3.20753 6.91042 .303030 3.31 3.32 3.33 10.9561 11.0224 11.0889 1.81934 1.82209 1.82483 5.75326 5.76194 5.77062 36.2647 36.5944 36.9260 1.49031 1.49181 1.49330 3.21077 3.21400 3.21722 6.91740 6.92436 6.93130 .302115 .301205 .300300 3.34 3.35 3.36 11.1556 11.2225 11.2896 1.82757 1.83030 1.83303 5.77927 5.78792 5.79655 37.2597 37.5954 37.9331 1.49480 1.49629 1.49777 3.22044 3.22365 3.22686 6.93823 6.94515 6.95205 .299401 .298507 .297619 3.37 3.38 3.39 11.3569 11.4244 11.4921 1.83576 1.83848 1.84120 5.80517 5.81378 5.82237 38.2728 38.6145 38.9582 1.49926 1.50074 1.50222 3.23006 3.23325 3.23643 6.95894 6.96582 6.97268 .296736 .295858 .294985 3.40 11.5600 1.84391 5.83095 39.3040 1.50369 3.23961 6.97953 .294118 3.41 3.42 3.43 11.6281 11.6964 11.7649 1.84662 1.84932 1.85203 5.83952 5.84808 5.85662 39.6518 40.0017 40.3536 1.50517 1.50664 1.50810 3.24278 3.24595 3.24911 6.98637 6.99319 7.00000 .293255 .292398 .291545 3.44 3.45 3.46 11.8336 11.9025 11.9716 1.85472 1.85742 1.86011 5.86515 5.87367 5.88218 40.7076 41.0636 41.4217 1.50957 1.51103 1.51249 3.25227 3.25542 3.25856 7.00680 7.01358 7.02035 .290698 .289855 .289017 3.47 3.48 3.49 12.0409 12.1104 12.1801 1.86279 1.86548 1.86815 5.89067 5.89915 5.90762 41.7819 42.1442 42.5085 1.51394 1.51540 1.51685 3.26169 3.26482 3.26795 7.02711 7.03385 7.04058 .288184 .287356 .286533 3.50 12.2500 1.87083 5.91608 42.8750 1.51829 3.27107 7.04730 .285714 n n 2 V^ A/IoTi fl 3 31 Vn sfto~^ ^lOOn 1/n VI] Powers Roots Reciprocals 99 n n 2 v^: VIoTi n 3 31 Vn ^10 n ^100 n 1/M 3.50 12.2500 1.87083 5.91608 42.8750 1.51829 3.27107 7.04730 .285714 3.51 3.52 3.53 12.3201 12.3904 12.4609 1.87350 1.87617 1.87883 5.92453 5.93296 5.94138 43:2436 43.6142 43.9870 1.51974 1.52118 1.52262 3.27418 3.27729 3.28039 7.05400 7.06070 7.06738 .284900 .284091 .283286 3.54 3.55 3.56 12.5316 12.6025 12.6736 1.88149 1.88414 1.88680 5.94979 5.95819 5.96657 44.3619 44.7389 45.1180 1.52406 1.52549 1.52692 3.28348 3.28657 3.28965 7.07404 7.08070 7.08734 .282486 .281690 .280899 3.57 3.58 3.59 12.7449 12.8164 12.8881 1.88944 1.89209 1.89473 5.97495 5.98331 5.99166 45.4993 45.8827 46.2683 1.52835 1.52978 1.53120 3.29273 3.29580 3.29887 7.09397 7.10059 7.10719 .280112 .279330 .278552 3.60 12.9800 1.89737 6.00000 46.6560 1.53262 3.30193 7.11379 .277778 3.61 3.62 3.63 13.0321 13.1044 13.1769 1.90000 1.90263 1.90526 6.00833 6.01664 6.02495 47.0459 47.4379 47.8321 1.53404 1.53545 1.53686 3.30498 3.30803 3.31107 7.12037 7.12694 7.13349 .277008 .276243 .275482 3.64 3.65 3.66 13.2496 13.3225 13.3956 1.90788 1.91050 1.91311 6.03324 6.04152 6.04979 48.2285 48.6271 49.0279 1.53827 1.53968 1.54109 3.31411 3.31714 3.32017 7.14004 7.14657 7.15309 .274725 .273973 .273224 3.67 3.68 3.69 13.4689 13.5424 13.6161 1.91572 1.91833 1.92094 6.05805 6.06630 6.07454 49.4309 49.8360 50.2434 1.54249 1.54389 1.54529 3.32319 3.32621 3.32922 7.15960 7.16610 7.17258 .272480 .271739 .271003 3.70 13.6900 1.92354 6.08276 50.6530 1.54668 3.33222 7.17905 .270270 3.71 3.72 3.73 13.7641 13.8384 13.9129 1.92614 1.92873 1.93132 6.09098 6.09918 6.10737 51.0648 51.4788 51.8951 1.54807 1.54946 1.55085 3.33522 3.33822 3.34120 7.18552 7.19197 7.19840 .269542 .268817 .263097 3.74 3.75 3.76 13.9876 14.0625 14.1376 1.93391 1.93649 1.93907 6.11555 6.12372 6.13188 52.3136 52.7344 53.1574 1.55223 1.55362 1.55500 3.34419 3.34716 3.35014 7.20483 7.21125 7.21765 .267380 .266667 .265957 3.77 3.78 3.79 14.2129 14.2884 14.3641 1.94165 1.94422 1.94679 6.14003 6.14817 6.15630 53.5826 54.0102 54.4399 1.55637 1.55775 1.55912 3.35310 3.35607 3.35902 7.22405 7.23043 7.23680 .265252 .264550 .263852 3.80 14.4400 1.94936 6.16441 54.8720 1.56049 3.36198 7.24316 .263158 3.81 3.82 3.83 14.5161 14.5924 14.6689 1.95192 1.95448 1.95704 6.17252 6.18061 6.18870 55.3063 55.7430 56.1819 1.56186 1.56322 1.56459 3.36492 3.36786 3.37080 7.24950 7.25584 7.26217 .262467 .261780 .261097 3.84 3.85 3.86 14.7456 14.8225 14.8996 1.95959 1.96214 1.96469 6.19677 6.20484 6.21289 56.6231 57.0666 57.5125 1.56595 1.56731 1.56866 3.37373 3.37666 3.37958 7.26848 7.27479 7.28108 .260417 .259740 .259067 3.87 3.88 3.89 14.9769 15.0544 15.1321 1.96723 1.96977 1.97231 6.22093 6.22896 6.23699 57.9606 58.4111 58.8639 1.57001 1.57137 1.57271 3.38249 3.38540 3.38831 7.28736 7.29363 7.29989 .258398 .257732 .257069 3.90 15.2100 1.97484 6.24500 59.3190 1.57406 3.39121 7.30614 .256410 3.91 3.92 3.93 15.2881 15.3664 15.4449 1.97737 1.97990 1.98242 6.25300 6.26099 6.26897 59.7765 60.2363 60.6985 1.57541 1.57675 1.57809 3.39411 3.39700 3.39988 7.31238 7.31861 7.32483 .255754 .255102 .254453 3.94 3.95 3.96 15.5236 15.6025 15.6816 1.98494 1.98746 1.98997 6.27694 6.28490 6.29285 61.1630 61.6299 62.0991 1.57942 1.58076 1.58209 3.40277 3.40564 3.40851 7.33104 7.33723 7.34342 .253807 .253165 .252525 3.97 3.98 3.99 15.7609 15.8404 15.9201 1.99249 1.99499 1.99750 6.30079 6.30872 6.31664 62.5708 63.0448 63.5212 1.58342 1.58475 1.58608 3.41138 3.41424 3.41710 7.34960 7.35576 7.36192 .251889 .251256 .250627 4.00 16.0000 2.00000 6.32456 64.0000 1.58740 3.41995 7.36806 .250000 n n 2 V^ VlO n n 3 31 Vrc ^10^ \ r LOO~^ 1/n 100 Powers Roots Reciprocals [VI n n 2 Vn VIo^ n 3 Jn VlOn ^100 n l/n 4.00 16.0000 2.00000 6.32456 64.0000 1.58740 3.41995 7.30806 .250000 4.01 4.02 4.03 16.0801 16.1604 16.2409 2.00250 2.00499 2.00749 6.33246 6.34035 6.34823 64.4812 64.9648 65.4508 1.58872 1.59004 1.59136 3.42280 3.42564 3.42848 7.37420 7.38032 7.38644 .249377 .248756 .248139 4.04 4.05 4.06 16.3216 16.4025 16.4836 2.00998 2.01246 2.01494 6.35610 6.36396 6.37181 65.9393 66.4301 66.9234 1.59267 1.59399 1.59530 3.43131 3.43414 3.43697 7.39254 7.39864 7.40472 .247525 .246914 .246305 4.07 4.08 4.09 16.5649 16.6464 16.7281 2.01742 2.01990 2.02237 6.37966 6.38749 6.39531 67.4191 67.9173 68.4179 1.59661 1.59791 1.59922 3.43979 3.44260 3.44541 7.41080 7.41686 7.42291 .245700 .245098 .244499 4.10 16.8100 2.02485 6.40312 68.9210 1.60052 3.44822 7.42896 .243902 4.11 4.12 4.13 16.8921 16.9744 17.0569 2.02731 2.02978 2.03224 6.41093 6.41872 6.42651 69.4265 69.9345 70.4450 1.60182 1.60312 1.60441 3.45102 3.45382 3.45661 7.43499 7.44102 7.44703 .243309 .242718 .242131 4.14 4.15 4.16 17.1396 17.2225 17.3056 2.03470 2.03715 2.03961 6.43428 6.44205 6.44981 70.9579 71.4734 71.9913 1.60571 1.60700 1.60829 3.45939 3.4G218 3.46496 7.45304 7.45904 7.46502 .241546 .240964 .240385 4.17 4.18 4.19 17.3889 17.4724 17.5561 2.04206 2.04450 2.04695 6.45755 6.46529 6.47302 72.5117 73.0346 73.5601 1.60958 1.61086 1.61215 3.46773 3.47050 3.47327 7.47100 7.47697 7.48292 .239808 .239234 .238663 4.20 17.6400 2.04939 6.48074 74.0880 1.61343 3.47603 7.48887 .238095 4.21 4.22 4.23 17.7241 17.8084 17.8929 2.05183 2.05426 2.05670 6.48845 6.49615 6.50384 74.6185 75.1514 75.6870 1.61471 1.61599 1.61726 3.47878 3.48154 3.48428 7.49481 7.50074 7.50666 .237530 .236967 .236407 4.24 4.25 4.26 17.9776 18.0625 18.1476 2.05913 2.06155 2.06398 6.51153 6.51920 6.52687 76.2250 76.7656 77.3088 1.61853 1.61981 1.62108 3.48703 3.48977 3.49250 7.51257 7.51847 7.52437 .235849 .235294 .234742 4.27 4.28 4.29 18.2329 18.3184 18.4041 2.06640 2.06882 2.07123 6.53452 6.54217 6.54981 77.8545 78.4028 78.9536 1.62234 1.62361 1.62487 3.49523 3.49796 3.50068 7.53025 7.53612 7.54199 .234192 .233645 .233100 4.30 18.4900 2.07364 6.55744 79.5070 1.62613 3.50340 7.54784 .232558 4.31 4.32 4.33 18.5761 18.6624 18.7489 2.07605 2.07846 2.08087 6.56506 6.57267 6.58027 80.0630 80.6216 81.1827 1.62739 1.62865 1.62991 3.50611 3.50882 3.51153 7.55369 7.55953 7.56535 .232019 .231481 .230947 4.34 4.35 4.36 18.8356 18.9225 19.0096 2.08327 2.08567 2.08806 6.58787 6.59545 6.60303 81.7465 82.3129 82.8819 1.63116 1.63241 1.63366 3.51423 3.51692 3.51962 7.57117 7.57698 7.58279 .230415 .229885 .229358 4.37 4.38 4.39 19.0969 19.1844 19.2721 2.09045 2.09284 2.09523 6.61060 6.61816 6.62571 83.4535 84.0277 84.6045 1.63491 1.63619 1.63740 3.52231 3.52499 3.52767 7.58858 7.59436 7.60014 .228833 .228311 .227790 4.40 19.3600 2.09762 6.63325 85.1840 1.63864 3.53035 7.60590 .227273 4.41 4.42 4.43 19.4481 19.5364 19.6249 2.10000 2.10238 2.10476 6.64078 6.64831 6.65582 85.7661 86.3509 86.9383 1.63988 1.64112 1.64236 3.53302 3.53569 3.53835 7.61166 7.61741 7.62315 .226757 .226244 .225734 4.44 4.45 4.46 19.7136 19.8025 19.8916 2.10713 2.10950 2.11187 6.66333 6.67083 6.67832 87.5284 88.1211 88.7165 1.64359 1.64483 1.64606 3.54101 3.54367 3.54632 7.62888 7.63461 7.64032 .225225 .224719 .224215 4.47 4.48 4.49 19.9809 20.0704 20.1001 2.11424 2.11660 2.11896 6.68581 6.69328 6.70075 89.3146 89.9154 90.5188 1.64729 1.64851 1.64974 3.54897 3.55162 3.55426 7.64603 7.65172 7.65741 .223714 .223214 .222717 4.50 20.2500 2.12132 6.70820 91.1250 1.65096 3.55689 7.66309 .222222 71 /I 2 V^ VlOn n 3 31 Vn ^ToTi \Too~^ l/n VI] Powers Roots Reciprocals 101 n n 2 V^ \IolI n 3 ^n \!0n ^100 n 1/n 4.50 20.2500 2.12132 6.70S20 91.1250 1.65096 3.55689 7.66309 .222222 4.51 4.52 4.53 20.3401 20.4304 20.5209 2.12368 2.12603 2.12838 6.71565 6.72309 6.73053 91.7339 92.3454 92.9597 1.65219 1.65341 1.65462 3.55953 3.56215 3.56478 7.66877 7.67443 7.68009 .221729 .221239 .220751 4.54 4.55 4.56 20.6116 20.7025 20.7936 2.13073 2.13307 2.13542 6.73795 6.74537 6.75278 93.5767 94.1964 94.8188 1.65584 1.65706 1.65827 3.56740 3.57002 3.57263 7.68573 7.69137 7.69700 .220264 .219780 .219298 4.57 4.58 4.59 20.8849 20.9764 21.0681 2.13776 2.14009 2.14243 6.76018 6.76757 6.77495 95.4440 96.0719 96.7026 1.65948 1.66069 1.66190 3.57524 3.57785 3.58045 7.70262 7.70824 7.71384 .218818 .218341 .217865 4.60 21.1600 2.14476 6.78233 97.3360 1.66310 3.58305 7.71944 .217391 4.61 4.62 4.63 21.2521 21.3444 21.4369 2.14709 2.14942 2.15174 6.78970 6.79706 6.80441 97.9722 98.6111 99.2528 1.66431 1.66551 1.66671 3.58564 3.58823 3.59082 7.72503 7.73061 7.73619 .216920 .216450 .215983 4.64 4.65 4.66 21.5296 21.6225 21.7156 2.15407 2.15639 2.15870 6.81175 6.81909 6.82642 99.8973 100.545 101.195 1.66791 1.66911 1.67030 3.59340 3.59598 3.59856 7.74175 7.74731 7.75286 .215517 .215054 .214592 4.67 4.68 4.69 21.8089 21.9024 21.9961 2.16102 2.16333 2.16564 6.83374 6.84105 6.84836 101.848 102.503 103.162 1.67150 1.67269 1.67388 3.60113 3.60370 3.60626 7.75840 7.76394 7.76946 .214133 .213675 .213220 4.70 22.0900 2.16795 6.85565 103.823 1.67507 3.60883 7.77498 .212766 4.71 4.72 4.73 22.1841 22.2784 22.3729 2.17025 2.17256 2.17486 6.86294 6.87023 6.87750 ] 04.487 105.154 105.824 1.67626 1.67744 1.67863 3.61138 3.61394 3.61649 7.78049 7.78599 7.79149 .212314 .211864 .211416 4.74 4.75 4.76 22.4676 22.5625 22.6576 2.17715 2.17945 2.18174 6.88477 6.89202 6.89928 106.496 107.172 107.850 1.67981 1.68099 1.68217 3.61903 3.62158 3.62412 7.79697 7.80245 7.80793 .210970 .210526 .210084 4.77 4.78 4.79 22.7529 22.8484 22.9441 2.18403 2.18632 2.18861 6.90652 6.91375 6.92098 108.531 109.215 109.902 1.68334 1.68452 1.68569 3.62665 3.62919 3.63172 7.81339 7.81885 7.82429 .209644 .209205 .208768 4.80 23.0400 2.19089 6.92820 110.592 1.68687 3.63424 7.82974 .208333 4.81 4.82 4.83 23.1361 23.2324 23.3289 2.19317 2.19545 2.19773 6.93542 6.94262 6.94982 111.285 111.980 112.679 1.68804 1.68920 1.69037 3.63676 3.63928 3.64180 7.83517 7.84059 7.84601 .207900 .207469 .207039 4.84 4.85 4.86 23.4256 23.5225 23.6196 2.20000 2.20227 2.20454 6.95701 6.96419 6.97137 113.380 114.084 114.791 1.69154 1.69270 1.69386 3.64431 3.64682 3.64932 7.85142 7.85683 7.86222 .206612 .206186 .205761 4.87 4.88 4.89 23.7169 23.8144 23.9121 2.20681 2.20907 2.21133 6.97854 6.98570 6.99285 115.501 116.214 116.930 1.69503 1.69619 1.69734 3.65182 3.65432 3.65681 7.86761 7.87299 7.87837 .205339 .204918 .204499 4.90 24.0100 2.21359 7.00000 117.649 1.69850 3.65931 7.88374 .204082 4.91 4.92 4.93 24.1081 24.2064 24.3049 2.21585 2.21811 2.22036 7.00714 7.01427 7.02140 118.371 119.095 119.823 1.69965 1.70081 1.70196 3.66179 3.66428 3.66676 7.88909 7.89445 7.89979 .203666 .203252 .202840 4.94 4.95 4.96 24.4036 24.5025 24.6016 2.22261 2.22486 2.22711 7.02851 7.03562 7.04273 120.554 121.287 122.024 1.70311 1.70426 1.70540 3.66924 3.67171 3.67418 7.90513 7.91046 7.91578 .202429 .202020 .201613 4.97 4.98 4.99 24.7009 24.8004 24.9001 2.22935 2.23159 2.23383 7.04982 7.05691 7.06399 122.763 123.506 124.251 1.70655 1.70769 1.70884 3.67665 3.67911 3.68157 7.92110 7.92641 7.93171 .201207 .200803 .200401 5.00 25.0000 2.23607 7.07107 125.000 1.70998 3.68403 7.93701 .200000 n n 2 Vn AloTI nj 31 Vn \1oTI xlOO n 1/n 102 Powers Roots Reciprocals [VI n n 2 V VlOn n 3 31 Vn ^ToTl S^IOO /I l/n 5.00 25.0000 2.23607 7.07107 125.000 1.70998 3.68403 7.93701 .200000 5.01 5.02 5.03 25.1001 25.2004 25.3009 2.23830 2.24054 2.24277 7.07814 7.08520 7.09225 125.752 126.506 127.264 1.71112 1.71225 1.71339 3.68649 3.68894 3.69138 7.94229 7.94757 7.95285 .199601 .199203 .198807 5.04 5.05 5.06 25.4016 25.5025 25.6036 2.24499 2.24722 2.24944 7.09930 7.10634 7.11337 128.024 128.788 129.554 1.71452 1.71566 1.71679 3.69383 3.69627 3.69871 7.95811 7.96337 7.96863 .198413 .198020 .197628 5.07 5.08 5.09 25.7049 25.8064 25.9081 2.25167 2.25389 2.25610 7.12039 7.12741 7.13442 130.324 131.097 131.872 1.71792 1.71905 1.72017 3.70114 3.70357 3.70600 7.97387 7.97911 7.98434 .197239 .196850 .196464 5.10 26.0100 2.25832 7.14143 132.651 1.72130 3.70843 7.98957 .196078 5.11 5.12 5.13 26.1121 26.2144 26.3169 2.26053 2.26274 2.26495 7.14843 7.15542 7.16240 133.433 134.218 135.006 1.72242 1.72355 1.72467 3.71085 3.71327 3.71569 7.99479 8.00000 8.00520 .195695 .195312 .194932 5.14 5.15 5.16 26.4196 26.5225 26.6256 2.26716 2.26936 2.27156 7.16938 7.17635 7.18331 135.797 136.591 137.388 1.72579 1.72691 1.72802 3.71810 3.72051 3.72292 8.01040 8.01559 8.02078 .194553 .194175 .193798 5.17 5.18 5.19 26.7289 26.8324 26.9361 2.27376 2.27596 2.27816 7.19027 7.19722 7.20417 138.188 138.992 139.798 1.72914 1.73025 1.73137 3.72532 3.72772 3.73012 8.02596 8.03113 8.03629 .193424 .193050 .192678 5.20 27.0400 2.28035 7.21110 140.608 1.73248 3.73251 8.04145 .192308 5.21 5.22 5.23 27.1441 27.2484 27.3529 2.28254 2.28473 2.28692 7.21803 7.22496 7.23187 141.421 142.237 143.056 1.73359 1.73470 1.73580 3.73490 3.73729 3.73968 8.04660 8.05175 8.05689 .191939 .191571 .191205 5.24 5.25 5.26 27.4576 27.5625 27.6676 2.28910 2.29129 2.29347 7.23878 7.24569 7.25259 143.878 144.703 145.532 1.73691 1.73801 1.73912 3.74206 3.74443 3.74681 8.06202 8.06714 8.07226 .190840 .190476 .190114 5.27 5.28 5.29 27.7729 27.8784 27.9841 2.29565 2.29783 2.30000 7.25948 7.26636 7.27324 146.363 147.198 148.036 1.74022 1.74132 1.74242 3.74918 3.75155 3.75392 8.07737 8.08248 8.08758 .189753 .189394 .189036 5.30 28.0900 2.30217 7.28011 148.877 1.74351 3.75629 8.09267 .188679 5.31 5.32 5.33 28.1961 28.3024 28.4089 2.30434 2.30651 2.30868 7.28697 7.29383 7.30068 149.721 150.569 151.419 1.74461 1.74570 1.74680 3.75865 3.76101 3.76336 8.09776 8.10284 8.10791 .188324 .187970 .187617 5.34 5.35 5.36 28.5156 28.6225 28.7296 2.31084 2.31301 2.31517 7.30753 7.31437 7.32120 152.273 153.130 153.991 1.74789 1.74898 1.75007 3.76571 3.76806 3.77041 8.11298 8.11804 8.12310 .187266 .186916 .186567 5.37 5.38 5.39 28.8369 28.9444 29.0521 2.31733 2.31948 2.32164 7.32803 7.33485 7.34166 154.854 155.721 156.591 1.75116 1.75224 1.75333 3.77275 3.77509 3.77743 8.12814 8.13319 8.13822 .186220 .185874 .185529 5.40 29.1600 2.32379 7.34847 157.464 1.75441 3.77976 8.14325 .185185 5.41 5.42 5.43 29.2681 29.3764 29.4849 2.32594 2.32809 2.33024 7.35527 7.36206 7.36885 158.340 159.220 160.103 1.75549 1.75657 1.75765 3.78209 3.78442 3.78675 8.14828 8.15329 8.15831 .184843 .184502 .184162 5.44 5.45 5.46 29.5936 29.7025 29.8116 2.33238 2.33452 2.33666 7.37564 7.38241 7.38918 160.989 161.879 162.771 1.75873 1.75981 1.76088 3.78907 3.79139 3.79371 8.16331 8.16831 8.17330 .183824 .183486 .183150 5.47 5.48 5.49 29.9209 30.0304 30.1401 2.33880 2.34094 2.34307 7.39594 7.40270 7.40945 163.667 164.567 165.469 1.76196 1.76303 1.76410 3.79603 3.79834 3.80065 8.17829 8.18327 8.18824 .182815 .182482 .182149 5.50 30.2500 2.34521 7.41620 166.375 1.76517 3.80295 8.19321 .181818 n n 2 V^ VTo~rT n 3 3 / Vn 1/WTi ShOO n l/n VI] Powers Roots Reciprocals 103 n n 2 ^ VlO n n 3 31 \n \ 10 n ^100 n l/n 5.50 30.2500 2.34521 7.41620 166.375 1.76517 3.80295 8.19321 .181818 5.51 5.52 5.53 30.3601 30.4704 30.5809 2.34734 2.34947 2.35160 7.42294 7.42967 7.43640 167.284 168.197 169.112 1.76624 1.76731 1.76838 3.80526 3.80756 3.80985 8.19818 8.20313 8.20808 .181488 .181159 .180832 5.54 5.55 5.56 30.6916 30.8025 30.9136 2.35372 2.35584 2.35797 7.44312 7.44983 7.45654 170.031 170.954 171.880 1.76944 1.77051 1.77157 3.81215 3.81444 3.81673 8.21303 8.21797 8.22290 .180505 .180180 .179856 5.57 5.58 5.59 31.0249 31.1364 31.2481 2.36008 2.36220 2.36432 7.46324 7.46994 7.47663 172.809 173.741 174.677 1.77263 1.77369 1.77475 3.81902 3.82130 3.82358 8.22783 8.23275 8.23766 .179533 .179211 .178891 5.60 31.3600 2.36643 7.48331 175.616 1.77581 3.82586 8.24257 .178571 5.61 5.62 5.63 31.4721 31.5844 31.6969 2.36854 2.37065 2.37276 7.48999 7.49667 7.50333 176.558 177.504 178.454 1.77686 1.77792 1.77897 3.82814 3.83041 3.83268 8.24747 8.25237 8.25726 .178253 .177936 .177620 5.64 5.65 5.66 31.8096 31.9225 32.0356 2.37487 2.37697 2.37908 7.50999 7.51665 7.52330 179.406 180.362 181.321 1.78003 1.78108 1.78213 3.83495 3.83722 3.83948 8.26215 8.26703 8.27190 .177305 .176991 .176678 5.67 5.68 5.69 32.1489 32.2624 32.3761 2.38118 2.38328 2.38537 7.52994 7.53658 7.54321 182.284 183.250 184.220 1.78318 1.78422 1.78527 3.84174 3.l 9198 6571 6711 6851 7962 8100 8238 9334 9470 9606 6991 7130 7269 8376 8513 8650 9742 9877*0013 7.4 7.5 7.6 2.0 0148 1490 2815 0283 0418 0553 1624 1757 1890 2946 3078 3209 0687 0821 0956 2022 2155 2287. 3340 3471 3601 1089 1223 1357 2419 2551 2683 3732 3862 3992 7.7 7.8 7.9 4122 5412 6686 4252 4381 4511 5540 5668 5796 6813 6939 7065 4640 4769 4898 5924 6051 6179 7191 7317 7443 5027 5156 5284 6306 6433 6560 7568 7694 7819 8.0 7944 8069 8194 8318 8443 8567 8691 8815 8939 9063 8.1 8.2 8.3 9186 2.1 0413 1626 9310 9433 9556 0535 0657 0779 1746 1866 1986 9679 9802 9924 0900 1021 1142 2106 2226 2346 *0047 *0169 *0291 1263 1384 1505 2465 2585 2704 8.4 8.5 8.6 2823 4007 5176 2942 3061 3180 4124 4242 4359 5292 5409 5524 3298 3417 3535 4476 4593 4710 5640 5756 5871 3653 3771 3889 4827 4943 5060 5987 6102 6217 8.7 8.8 8.9 6332 7475 8605 6447 6562 6677 7589 7702 7816 8717 8830 8942 6791 6905 7020 7929 8042 8155 9054 9165 9277 7134 7248 7361 8267 8380 8493 9389 9500 9611 9.0 9722 9834 9944*0055 *0166 *0276 *0387 *0497 *0607 *0717 9.1 9.2 9.3 2.2 0827 1920 3001 0937 1047 1157 2029 2138 2246 3109 3216 3324 1266 1375 1485 2354 2462 2570 3431 3538 3645 1594 1703 1812 2678 2786 2894 3751 3858 3965 9.4 9.5 9.6 4071 5129 6176 4177 4284 4390 5234 5339 5444 6280 6384 6488 4496 4601 4707 5549 5654 5759 6592 6696 6799 4813 4918 5024 5863 5968 6072 6903 7006 7109 9.7 9.8 9.9 7213 8238 9253 7316 7419 7521 8340 8442 8544 9354 9455 9556 7624 7727 7829 8646 8747 8849 9657 9757 9858 7932 8034 8136 8950 9051 9152 9958 *0058 *0158 10.0 2.3 0259 0358 0458 0558 0658 0757 0857 0956 1055 1154 N 123 456 789 114 Napierian or Natural Logarithms 10 to 99 [VII 10 2.30259 25 3.21888 40 3.68888 55 4.00733 70 4.24850 85 4.44265 11 12 13 14 2.39790 2.48491 2.56495 2.63906 26 27 28 29 3.25810 3.29584 3.33220 3.36730 41 42 43 44 3.71357 3.73767 3.76120 3.78419 56 57 58 59 4.02535 4.04305 4.06044 4.07754 71 72 73 74 4.26268 4.27667 4.29046 4.30407 86 87 88 89 4.45435 4.46591 4.47734 4.48864 15 2.70805 30 3.40120 45 3.80666 60 4.09434 75 4.31749 90 4.49981 16 17 18 19 2.77259 2.83321 2.89037 2.94444 31 32 33 34 3.43399 3.46574 3.49651 3.52636 46 47 48 49 3.82864 3.85015 3.87120 3.89182 61 62 63 64 4.11087 4.12713 4.14313 4.15888 76 77 78 79 4.33073 4.34381 4.35671 4.36945 91 92 93 94 4.51086 4.52179 4.53260 4.54329 20 2.99573 35 36 37 38 39 3.55535 50 3.91202 65 4.17439 80 4.38203 95 4.55388 21 22 23 24 3.04452 3.09104 3.13549 3.17805 3.58352 3.61092 3.63759 3.66356 51 52 53 54 3.93183 3.95124 3.97029 3.98898 66 67 68 69 4.18965 4.20469 4.21951 4.23411 81 82 83 84 4.39445 4.40672 4.41884 4.43082 96 97 98 99 4.56435 4.57471 4.58497 4.59512 Napierian or Natural Logarithms 100 to 409 N 123 456 789 10 4.6 0517 1512 2497 3473 4439 5396 6344 7283 8213 9135 11 12 13 4.7 0048 8749 4.8 6753 0953 1850 2739 9579 *0402 *1218 7520 8280 9035 3620 4493 5359 *2028 *2831 *3628 9784 *0527 *1265 6217 7068 7912 *4419 *5203 *5981 *1998 *2725 *3447 14 15 16 4.9 4164 5.0 1064 7517 4876 5583 6284 1728 2388 3044 8140 8760 9375 6981 7673 8361 3695 4343 4986 9987 *0595 *1199 9043 9721 *0395 6625 6260 6890 *1799 *2396 *2990 17 18 19 5.1 3580 9296 5.2 4702 4166 4749 5329 9850 *0401 *0949 5227 5750 6269 5906 6479 7048 *1494 *2036 *2575 6786 7300 7811 7615 8178 8739 *3111 *3644 *4175 8320 8827 9330 20 9832 *0330 *0827 *1321 *1812 *2301 *2788 *3272 *3754 *4233 21 22 23 5.34711 9363 5.4 3808 5186 5659 6129 9816 *0268 *0717 4242 4674 5104 6598 7064 7528 *1165 *1610 *2053 5532 5959 6383 7990 8450 8907 *2495 *2935 *3372 6806 7227 7646 24 25 26 8064 6.5 2146 6068 8480 8894 9306 2545 2943 3339 6452 6834 7215 9717 *0126 *0533 3733 4126 4518 7595 7973 8350 *0939 *1343 *1745 4908 5296 5683 8725 9099 9471 27 28 29 9842 5.6 3479 6988 *0212 *0580 *0947 3835 4191 4545 7332 7675 8017 *1313 *1677 *2040 4897 5249 5599 8358 8698 9036 *2402 *2762 *3121 6948 6296 6643 9373 9709*0044 30 5.7 0378 0711 1043 1373 1703 2031 2359 2685 3010 3334 31 32 33 3657 6832 9909 3979 4300 4620 7144 7455 7765 *0212 *0513 *0814 4939 6257 5574 8074 8383 8690 *1114 *1413 *1711 5890 6205 6519 8996 9301 9606 *2008 *2305 *2600 34 35 36 6.8 2895 5793 8610 3188 3481 3773 6079 6363 6647 8888 9164 9440 4064 4354 4644 6930 7212 7493 9715 9990*0263 4932 5220 5507 7774 8053 8332 *0536 *0808 *1080 37 38 39 6.9 1350 4017 6615 1620 1889 2158 4280 4542 4803 6871 7126 7381 2426 2693 2959 5064 6324 5584 7635 7889 8141 3225 3489 3754 5842 6101 6358 8394 8645 8896 40 9146 9396 9645 9894 *0141 *0389 *0635 *0881 *1127 *1372 N 123 456 789 Above 409, use the formula log, lOn = log, n + log, 10 or the formula log, n = log, 10-logio n = = log e n + 2.30258509, 2.30258509 logio n. vim Table VIII Multiples of M and of 1/M 115 AT N-M N N-M AT N -r- M N N -r-M 0.00000 000 50 21.71472410 0.00000 000 50 115.12925465 1 2 3 0.43429 448 0.86858 896 1.30288 345 51 52 53 22.14901 858 22.58331 306 23.01760 754 1 2 3 2.30258 509 4.60517 019 6.90775 528 51 52 53 117.43183974 119.73442484 122.03700 993 4 5 6 1.73717 793 2.17147241 2.60576 689 54 55 56 23.45190 202 23.88619 650 24.32049 099 4 5 6 9.21034 037 11.51292546 13.81551 056 54 55 56 124.33959 502 126.64218011 128.94476 521 7 8 9 3.04006 137 3.47435 586 3.90865 034 57 58 59 24.75478 547 25.18907 995 25.62337 443 7 8 9 16.11809 565 18.42068 074 20.72326 584 57 58 59 131.24735 030 133.54993 539 135.85252 049 10 4.34294 482 60 26.05766 891 10 23.02585 093 60 138.15510558 11 12 13 4.77723 930 5.21153378 5.64582 826 61 62 63 26.49196 340 26.92625 788 27.36055 236 11 12 13 25.32843 602 27.63102 112 29.93360 621 61 62 63 140.45769 067 142.76027 577 145.06286 086 14 15 16 6.08012 275 6.51441 723 6.94871 171 64 65 66 27.79484 684 28.22914 132 28.66343 581 14 15 16 32.23619 130 34.53877 639 36.84136 149 64 65 66 147.36544 595 149.66803 104 151.97061 614 17 18 19 7.38300 619 7.81730 067 8.25159 516 67 68 69 29.09773 029 29.53202 477 29.96631 925 17 18 19 39.14394 658 41.44653 167 43.74911 677 67 68 69 154.27320 123 156.57578 632 158.87837 142 20 8.68588 964 70 30.40061 373 20 46.05170 186 70 161.18095 651 21 22 23 9.12018412 9.55447 860 9.98877 308 71 72 73 30.83490 822 31.26920270 31.70349 718 21 22 23 48.35428 695 50.65687 205 52.95945 714 71 72 73 163.48354 160 165.78612 670 168.08871 179 24 25 26 10.42306 757 10.85736 205 11.29165653 74 75 76 32.13779 166 32.57208 614 33.00638 062 24 25 26 55.26204 223 57.56462 732 59.86721 242 74 75 76 170.39129 688 172.69388 197 174.99646 707 27 28 29 11.72595 101 12.16024 549 12.59453 998 77 78 79 33.44067511 33.87496 959 34.30926 407 27 28 29 62.16979 751 64.47238 260 66.77496 770 77 78 79 177.29905 216 179.60163 725 181.90422 235 30 13.02883 446 80 34.74355 855 30 69.07755 279 80 184.20680 744 31 32 33 13.46312 894 13.89742 342 14.33171 790 81 82 83 35.17785 303 35.61214752 36.04644 200 31 32 33 71.38013 788 73.68272 298 75.98530 807 81 82 83 186.50939 253 188.81197 763 191.11456272 34 35 36 14.76601 238 15.20030 687 15.63460 135 84 85 86 36.48073 648 36.91503 096 37.34932 544 34 35 36 78.28789 316 80.59047 825 82.89306 335 84 85 86 193.41714 781 195.71973 290 198.02231 800 37 38 39 16.06889 583 16.50319 031 16.93748 479 87 88 89 37.78361 993 38.21791 441 38.65220 889 37 38 39 40~ 85.19564 844 87.49823 353 89.80081 863 87 88 89 200.32490 309 202.62748 818 204.93007 328 40 17.37177 928 90 39.08650 337 92.10340 372 90 207.23265 837 41 42 43 17.80607 376 18.24036 824 18.67466 272 91 92 93 39.52079 785 39.95509 234 40.38938 682 41 42 43 94.40598 881 96.70857 391 99.01115900 91 92 93 209.53524 346 211.83782856 214.14041 365 44 45 46 19.10895 720 19.54325 169 19.97754 617 94 95 96 40.82368 130 41.25797 578 41.69227 026 44 45 46 101.31374 409 103.61632918 105.91891 428 94 95 96 216.44299 874 218.74558 383 221.04816 893 47 48 49 20.41184 065 20.84613 513 21.28042 961 97 98 99 42.12656474 42.56085 923 42.99515 371 47 48 49 108.22149 937 110.52408446 112.82666956 97 98 99 223.35075 402 225.65333911 227.95592 421 50 21.71472410 100 43.42944 819 50 115.12925465 100 230.25S50 930 M = logic e = .43429 44819 03251 82765 logio n = lc> n-logio e=M log e n. logio 457 6607 6761 6471 6622 6776 6486 6637 6792 6501 6653 6808 6516 6668 6823 6531 6683 6839 6546 6699 6855 6561 6714 6871 6577 6730 6887 6592 6745 6902 235 235 235 689 689 689 11 1214 11 1214 11 13 14 .84 .85 .86 6918 7079 7244 6934 7096 7261 6950 7112 7278 6966 7129 7295 6982 7145 7311 6998 7161 7328 7015 7178 7345 7031 7194 7362 7047 7211 7379 7063 7228 7396 235 235 235 7 810 7 810 7 810 11 13 15 12 13 15 12 14 15 .87 .88 .89 7413 7586 7762 7430 7603 7780 7447 7621 7798 7464 7638 7816 7482 7656 7834 7499 7674 7852 7516 7691 7870 7534 7709 -SS9 7551 7727 7907 7568 7745 "925 245 245 246 7 910 7911 7 911 12 14 16 12 14 16 13 15 16 .90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 246 7 911 13 15 17 .91 .92 .93 8128 8318 8511 8147 8337 8531 8166 8356 8551 8185 8375 8570 8204 8395 8590 8222 8414 8610 8241 8433 8630 8260 8453 8650 8279 8472 8670 8299 8492 8690 246 246 246 8911 81012 81012 13 15 17 14 15 17 14 16 18 .94 .95 .96 8710 8913 9120 8730 8933 9141 8750 8954 9162 8770 8974 9183 8790 8995 9204 8810 9016 9226 8831 9036 9247 8851 9057 9268 8872 9078 9290 8892 9099 9311 246 246 246 81012 81012 9 11 13 14 16 18 15 17 19 15 17 19 .97 .98 .99 9333 9550 9772 9354 9572 9795 9376 9594 9817 9397 9616 9840 9419 9638 9863 9441 9661 0886 9462 9683 9908 9484 9705 9931 9506 9727 9954 9528 9750 9977 246 247 257 91113 911 13 9 11 14 15 17 19 16 18 20 161821 138 Table XIV c Four Place Trigonometric Functions [XIV c [Characteristics of Logarithms omitted determine by the usual rule from the value] SINE TANGENT COTANGENT COSINE IADIANS DEGREES Value Logw Value Logio Value Logio Value Logio oono 0OO' noon - noon - i nfion onoo 90 00' 1 ^708 \J\S\J\J .0029 W 10 0029 .4637 \j\j\j\j .0029 .4637 343.77 .5363 \.*\j\j\j\j f\j\j\j\j 1.0000 .0000 vVf \J\J 50 i . > i \j - = - in strips = = = = j the EE 5 the 00 - - = m i (4) 4-V.^. -- tne -- N will = = work 1%.; inm i large < C I Q O a 'tf'i^-v-yt'