TRIGONOMETRIC TABLES REVISED EDITION PREPARED UNDER THE DIRECTION OF EARLE RAYMOND HEDRICK New York THE MACMILLAN COMPANY 1923 All rights reserved COPYRIGHT, 1913 and 1920, BY THE MACMILLAN COMPANY Set up and electrotyped. Revised edition published August, 1920. Norwood Press J. S. Cushing Co.- - Berwick & Smith Co. PREFACE THE present edition of this book contains several tables not contained in the previous editions. The probability of the occurrence of errors has been minimized by using electrotype reproductions of the tables previously included, even when changes were made. Remarkably few errors existed in the original edition; what few have been discovered have been corrected. Minor changes only occur in the earlier pages. Care has been taken to preserve the page numbers of the principal tables up to page 114, so that older editions may be used in class-work without confusion, and texts which contain the principal tables may be used in the same class. Among the minor changes are the insertion of a condensed table of logarithms and antilogarithms (Table Ia, p. 20), the insertion of a table of values of S and T for interpolation in logarithmic trigonometric functions (Table IIIa, p. 45), and the insertion on pages 1-19 of the logarithms of a few important numbers at appropriate points. The principal changes follow page 114. Tables VIII and IX (pp. 115– 122) make reasonably complete the tables of hyperbolic functions formerly represented only by Table XII (pp. 112–114): These functions are of increasing importance, notably in Electrical Engineering. The table of haversines (Table X, pp. 123-125) will be welcomed particularly by those interested in navigation. The table of factors of composite numbers and logarithms of primes (Table XI, pp. 126-127) has obvious uses. Tables XII a, b, c, d, e, ƒ, pages 128-132, are intended for work involving compound interest, annuities, depreciation, etc. They will be useful for statistics, insurance, accounting, and the mathematics of business. The same care has been exercised to eliminate errors in the new tables that resulted in so great a degree of reliability in the original edition of these tables. E. R. HEDRICK. V EXPLANATION OF THE TABLES * TABLE I. FIVE-PLACE COMMON LOGARITHMS OF NUMBERS FROM 1 TO 10 000 1. Powers of 10. Consider the following table of values of powers of 10: This table may be used for multiplying or dividing powers of 10, by means of the rules 10a. 106 = 10a+b, 10a ÷ 106 = 10a-b. Thus, to multiply 1000 by 100,000, add the exponent of 10 in column A opposite 1000 to the exponent of 10 opposite 100,000: 3+ 5 = 8; and look for the number in column B opposite 108, i.e. 100,000,000. Similarly 1,000,000 ×.0001 = 100, since 6+ (-4) = 2. To divide 1,000,000 by 100, from the exponent of 10 opposite 1,000,000 subtract the exponent of 10 opposite 100; 6 – 2 = 4; and look for the number opposite 104, i.e. 10,000. Similarly .001÷1,000,000=.000000001, since 3-6-9. To find the 4th power of 100, multiply the exponent of 10 opposite 100 by 4: 4 × 2 = 8, and look for the number opposite 108, i.e. 100,000,000. Likewise (.001)3 .000000001, since 3 × (−3) 9. To find the cube root of 1,000,000,000, divide the exponent of 10 opposite 1,000,000,000 by 3, 9 ÷ 3 = 3, and look for the number opposite 103. * This Explanation, written to accompany the five-place tables, may be used also for the four-place tables by omitting the last figure in each example in a manner obvious to the teacher. vii |