43 44 45 46 .86216 1.15987 .89306 47 .86267 1.15919 .89358 48 .86318 1.15851 .89410 49 .86368 1.15783 .89463 50 .86419 1.15715 .89515 41 .85963 1.16329 .89045 1.12303 .92224 1.08432 .95506 1.04705 .98901 1.01112 19 .98958 1.01053 18 .99016 1.00994 17 .99073 1.00935 16 .99131 1.00876 15 .99189 1.00818 14 .99247 1.00759 13 .99304 1.00701 12 .99362 1.00642 11 .99420 1.00583 10 60 51 .86470 1.15647 .89567 1.11648 .92763 .96288 1.03855 .99710 1.00291 .96344 1.03794 .99768 1.00233 .96400 1.03734 .99826 1.00175 .96457 1.03674 .99884 1.00116 1.03613 .99942 1.00058 1.03553 1.00000 1.00000 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 1.07801 .96064 1.04097 .99478 1.00525 .96120 1.04036 .99536 1.00467 .96176 1.03976 .99594 1.00408 .96232 1.03915 .99652 1.00350 1.07550 1.07487 1.07425 490 480 470 460 450 LOGARITHMIC TABLES To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle From 0° to 45°.-In the table entitled Logarithms of Trigonometric Functions, find the number of degrees at the top of the page, and the number of minutes in the left-hand column headed ('); opposite the latter, and under the proper head, find the desired logarithmic sine, cosine, tangent, or cotangent. To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle From 45° to 90°.-In the table entitled Logarithms of Trigonometric Functions, find the number of degrees at the bottom of the page, and the number of minutes in the right-hand column headed ('); opposite the latter, and above the proper head, find the desired logarithmic sine, cosine, tangent, or cotangent. To Find the Logarithmic Functions for an Angle Containing Degrees, Minutes, and Seconds. Find the logarithm for the degrees and minutes in the manner just given, then from the column headed d. take the number next below the logarithm thus found; under the heading P.P., find a column headed by this number, and find in this column the number opposite the given number of seconds; add it to the logarithm already found for the degrees and minutes. If the exact number of seconds is not given under P.P., the proper values may be found by interpolating between the values given. As the differences in the column headed d. represent differences corresponding to 60 sec., the amount to be added after the logarithm of the degrees and minutes has been found may be obtained by multiplying the difference by the number of seconds, and dividing the result by 60. The columns headed Cpl. S. and Cpl. T. on pages 1028 to 1030 can be used to find logarithms of angles including seconds less than 3° and greater than 86°. Reduce the degrees, minutes, and seconds to seconds, and use the following formulas, substituting for Cpl. S and Cpl. T. the values given in the table, and for S. and T., the difference between 10 and Cpl. S. and Cpl. T. as given. For angles less than 4°, log sin a = log a S.; log tang a = log a" + T.; log cotg a = Cpl. log a" + Cpl. T. Cpl. log tang a; log a" log sin a+ Cpl. S. = log tang a+ Cpl. T. = Cpl. log cotg a + Cpl. T. For angles greater than 86°, log cos a = = log (90° a'') + S.; log cótg a log (90° a") + T.; log tang a = Cpl. log (90° a'') + Cpl. T. = Cpl. log cotg a; log (90° a") log cos a + Cpl. S. log cotg a + Cpl. T. Cpl. log tang a + Cpl. T. = = = = = COMMON LOGARITHMS OF NUMBERS No. Log. No. Log. No. Log. No. Log. No. Log. 795 106 140 121 08 279 314 350 386 422 458 493 529 565 600 38 37 36 955 *307 656 123 830 864 899 934 968 *003 175 209 243 278 312 346 3.8 3.7 3.6 7.6 7.4 7.2 3 11.4 11.1 10.8 4 15.2 14.8 14.4 5 19.0 18.5 18.0 6 22.8 22.2 21.6 7 26.6 25.9 25.2 8 80.4 29 6 28.8 9 34.2 33.3 32.4 34133 354 386 418 672 704 735 767 138 988 *019 *051 *082 139 14 301 333 364 395 613 644 675 706 737 768 799 829 860 891 141 922 953 983 *014 *045 *076 *106 *137 *168 *198 142 15 229 259 290 320 351 381 412 442 473 503 1 3.2 3.1 3.0 143 534 564 594 625 655 685 715 746 776 806 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 16 137 167 197 227 256 286 316 346 376 406 4 12.8 12.4 12.0 146 435 465 495 524 554 584 613 643 673 702 147 732 761 791 820 850 879 909 938 148 17 026 056 085 114 143 173 202 149 319 348 377 406 435 464 150 609 638 667 290 322 513 545 577 609 640 799 830 862 893 925 956 *114 *145*176*208 *239 *270 426 457 489 520 551 582 967 997 7 22.4 21.7 21.0 231 260 289 8 25.6 24.8 24.0 493 522 551 580 9 28.8 27.9 27.0 782 811 840 869 182 26 007 031 055 079 102 183 245 269 293 184 482 505 529 185 717 741 186 189 126 150 174 316 340 364 387 553 576 600 623 647 670 694 764 788 811 834 858 881 905 928 951 975 998 *021 *045 *068 *091 *114 *138 *161 187 27 184 207 231 254 277 300 323 346 370 393 188 416 439 462 485 508 531 554 577 600 623 646 669 692 715 738 198 221 411 435 458 761 784 807 830 852 230 36 173 192 211 229 231 361 380 399 418 232 549 568 586 605 233 736 754 773 791 234 922 940 057 075 241 242 243 248 267 286 305 324 342 436 455 474 493 511 530 642 661 680 698 717 810 829 847 866 884 903 959 977 996 *014 *033 *051 *070 *088 235 37 107 125 144 162 181 199 218 236 291 310 328 346 365 383 401 237 475 493 511 530 548 238 658 676 694 712 731 239 840 858 876 894 912 240 38 021 039 202 220 238 256 274 292 310 328 346 364 382 399 417 435 453 471 489 507 525 543 561 578 596 614 632 650 668 686 703 721 244 739 757 775 792 810 828 846 863 881 899 245 917 934 952 970 987 *005 *023 *041 *058 *076 246 39 094 111 129 146 164 182 199 247 270 287 305 322 340 358 445 463 480 498 515 533 550 248 18 249 620 637 655 672 690 707 724 742 759 777 123456780 1.7 84 5.1 6.8 8.5 10.2 11.9 13.6 9 15.3 |