Six-Figure Tables of Trigonometric Functions

THE PRESENT six-figure trigonometric tables complete the series of tables of the natural values of the trigonometric functions published by Fizmatgiz. Now that small computers have become very widely available, almost all  computations are carried out by machine, and the majority of computational schemes arc suited to this purpose. The situation calls urgently for the availability of tables containing the natural values of all six trigonometric functions. The following special factor emerges here. In logarithmic computations the same relative accuracy is guaranteed more or less automatically for all values of the argument: the number of correct significant figures in the result is either equal to or (in rare cases) one less than, the number of significant figures in the mantissa of the logarithm. In computations with natural values of the functions the same relative accuracy is guaranteed in practice for all arguments only by having a constant nmber of significant figures throughout the tables. Until recently however, tables of the natural values of the trigonometric functions have been compiled both in Russia and abroad with the same number of places after the decimal point, which leads to a loss of accuracy when computing with functions of small angles. In view of this there is an urgent need for tables of the natural values of the trigonometric functions with a constant number of significant figures which substantially guarantees roughly the- same relative accuracy for all angles. The present tables, together with the following, already published by Fizmatgiz: Fil'e-figure Tables (L. S. Khrenov~ 1954), Five-.figure Tables l~,ith the Argument in Time (L. S. Khrenov, 1954), Seven-figure Tables(L. S. Khrenov, 1956) and Six-figure Tables with the Argunlent in Time (S. A. Angelov, 1957), form a complete series ~ith the same number of significant figures, satisfying the main requirements of a wide variety of computers. When compiling the present tables, use was made for purposes of collation of the following tables of the natural values of the trigonometric functions: The I)-figure Table..' of H. Andoyer, (Paris, 1915-1918), the Eight-figure Table of J. Peters (Berlin) J939), the Seven-figure Table of °L.S. Khrenov (2nd. ed., Gostekhizdat, 1956), the Seven-figure Table of H. C. Ives, and the Eight-figure Tables oj' the Logarith,l1.ft of NumberaV and oJ the Trigonometric functions of J. Bauschin.e;er and J. Peters (Geodezizdat, 1942 and 1944).