Apéndice

Tablal. Logaritmosdelosnúmeros

10 000011041412 079213 ]1~!)

.114 l.t ti ¡

1 2 3 4 I5 6 7 8 9 11 2 s\4 5 617 8 9

00.130086 0128 0170 0212 U253 0294 0334 0374 4 8-1~

1

17 21 ~5129 33 37,0.-1;;3 0492 0531 0569 \>607 (.1645 061:12 0719 0755 4 811 15 lO 23

1

26 30 34O~:!d 01'164 OHIJ,O 0034

,

Ofl(j!l 100.. 1038 1072 110<J 3 710

1

]417 21 2428:n

! 17:1' lZ06 1239 1271 n03, 1335 1367 1399 1430 3 610 13,16 191

23 2~ 291-1:~215~:J 15531584,1614 1644 16731703 17323 6 9 12 15 18 212427,

-25 :!!l7\J ,3997 4014 4031 40484065 4082 4099 41H> 4133 2 :} 5 7 910

1

1~ U 1526 4150 4166 4183 4200 4216 42~2 4249 ,4265 42~1 4298 2 3 5 7 810 11131527 431.4 4330 4346 4362 4378 4393 4409 4425 4440 4456 2 3 5 6 8 9

1

11 13 1428 4472 4487 4502 4518 4533 4548 456-i 4579 4594 4609 2 3 5 6 8 9 11 12 H

29 4624 4G39 4654 46G9 4683 4698 4713 4728 4742 4757 1 3 4 6 '7 9 1012.13

30 4771 4786 4800 48B 48294843 4857 4871 4i!86 4900 1 3 4 6 7 U1

10111331 4914 4928 4942 4955 496\) 1983 4997 5011 5024 51138 1 3 41 6 7. 81011 12

32 5051 5065 5079 5092 51055119 5132 5145 5159 5172 1 3 4

\

5 7 8 911 1233 5185 5198 5211 5224 5237 5250 5263 5276 52R9 5302 1 3 -1 5 6 ~ 9 10 12U 5315 5328 5340 5353 5366 fi378 539J '5403 5-H6 5428 1 3 41 5 6 8 91011

35 5441 5453 5465 5478 5490, 'i502 5S14 5527 5539 5551 1, 2 4

1

5 6 7 9 10'11 .,36 5563 5575 5587 5599 5611 5623 5635 5647 56

,

58 5670 1 2 4 5 6 7

1

8101137 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 1 2 3, 5 6 '7 8 91038 5798 5809 5821 5832 5843 5855 58ti6 5877 58..6.1'!51:19!) 1 2 3

1

5 6 7 8 ~ 10

S9 ,5'911 5922 5933 594_4 5955 5966 5977 5988 59!1!)üU] (1 l' ~ a 4. 5 71 8 9 1(t

40 6021 603l 6042 6053 6064 6975- 6085 6096 6107 6117 1 2 3j 4 5 G¡ 8 910n 6128 6138,6149 6160 6170 6180 6191 6201 6212 6222 1 2 3; 4 5 (i 1

1

7 8 !I

42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 1 2 31 4 5 G 7 8 9

43 6335 '6345 6355 6365 6375 6385 63~5 6405 6415 6425 1 2 ai 4 5 C.I 7 ~ 9U 6435 6444 6454 6464 6474 6484 6493,65.03 6513 6522 1 2 3 4. 5 (j I 7 8 9

45 6532 6542 6551 656165716580 6590 6599 6609 661~ 1 2 al 4 5 61

7 8 946 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 ~ 2 3 4 5 G 7 7 847 6721 67,30 6739 6749 6758 6767 6776 6785 6794 6803 1 2 a 4. 5 .;,

1

6 7 S

U 6812 6821 6880 6839 684.8 6857 6866 6875 6884 6893 1 2 3 4 4 5 6 7 849 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 1 2 3 <1 4 5 I 6 7 8

, '1:60 6990 6998' 7007 7016 70247033 7042 7050 7059 7067 1 2 3

\

3 4. 5 I 6 7 851 7076 706-i 7093 7101 '1110 7118 7126 7135 7143 7152 1 2 3 3 4 51 6 7 i!52 7160 7168 7177 7185 7~98 720~ 7210 7218 7226 7235 1 2 2

1

' 3 4 5 " 6 7 753 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 1 ~ 2 3 4 5 6 6 7

54 7324 7332 7~40, 7348 7356 7364 7:Jn 7'380 7388 739611 2 2 3 4 5,~

,11°'I O, 1 2 S 4 I 5 6 7 8 9 11 2 31 4 5. 61 7 ti !i i

285

15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 3 6 8 11 1417 20 22 25.-16 2041 068 2095 2122 214S 2175 2201 2227 2253 2279 3 5 8 11 13 16, 1821 2417.2301 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 5--7 101215 17202218 553 77 2601 2625 2648 2672 2695 2718 2742 2765 2 5 7 D 1 1-11.6192119 2788 2d10 2833 2856 2878 2900 2923 2945 2067 2989 2 4

7191113 161821>

3010 3032 3054 :j¡)75 ::096 3118 3139 3160 3181 320]I20 24681113115171921 3 243 326S 3184 3304 3324 3345 3365 3385 3404 2 4 6 8101:?,141618

22 3424 3411 3464 3483 3502 322 3541 3560 3579 359S 2 4 G 810 1::?114 1517

23 3617 :1636 3655 3674 3692 3711 :.:729 3747 37ti6 371:1.¡ 2 4 6 7 !) 11 i13 15 1724 :>802 3820 3838 3856 31:17413892 3909 3IJ27 3U45 3962 2 4 51 7 911 121-116

286

Tabla 1. logaritmos de los números

N I o , I 5,8 9 11 2 31' & 6 I 7 8 91 2 3 6 .,

&6 7404 t412 7419 7427 7435 7443 7451 7459 .,46666 7.82 7490 7497 7505 7513 7520 7528 7536 7543

677559 7568 7574 7582'75897597 7604 7612 7619

58 7684 7642 7849 7657 766~ 7672 7679 7686 769469 7709 7716 7723 7731 773~ 7745 7752 7760 7767

7474 17551 17627 17701 17774 1

,.

60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 1

61 7853 7860 7868 7875 7882 7889 7896 7993 7910 7917 1

62 7924 7931 7938 7945 7952 7959 7966 7973, 7980 7987 163 79038000 8007 8014 80218028 8035,8041 8048 8055 1

8' 80f,2806980758082808980G6&102 81098116 8122 '1

86 8129 8136 8142 8149 8156 8162 8169 8176 81.82 8189 1

68 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 ,167 8261 8267 8274 82808287 8293 8299 8306 8312 8319 168 83~5 8331 8338 8344 8351 8357 8363 8370 '8376 8382 169 8388 8395 8401 8407 8414 84~0 8426 8~32 84~9 8445 1

70 8451 8~57 8463 8470 8476 8482 8488 8494 8500 8506 171 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 1

72 8573 8579 8585 8591 8597 8603 8609 8&15 8621 8627 1

73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8~86 ~74 8692 8698 8704 8710 8'16 8722 8727 8733 8739 8745 1

75 A751 8756 8762 8768 8774 8779 8785 8791 8797 8802 176 8808 8814 8820 8825 8831 8831 8842 8848 88~4 8859 177 8865 881i 8876 8882 8887 8893 8899 8904 8910 8915 ~7~ 8921 8927 8932 8938 8943 89~9 8954 8960 8965 8971 1

79 8976 8982 8987 899~ 8998 9004 9009 9015 9020 9025 1

2 2132 2

1

82 2 31 2 31 2 3

4 5 5 6 74. 5 5 6 .,4. 5 5 6 74 " 5 6 7" " 5 6 7

12344. 566123445661.233456612884. 55612384 ~56

1233455612334. 55.61 2 8 3 4. 5 5 61233445612234456

1 2 21 2 21 2 21 2 21 2 2

3 4 4" 5 63 4 4 5 534455a 4 '45'S3"4.65

12233

1

4551 2 2 3 3 4 6'5122334461223'8'

1

44512238445

80 9031 9036 0042 9047 9'0539058 906:19069 9074 9079 1 1 2 2 3 3 4. 4, 681 9085 0090' 9096 9101 9106 9112 9117 9122 912R 0133 1 1. 22 3 3 4 4 582 9138 9143 9149 9154 91599165 9170 9175 9180 ~186 1 1 2 2 3 3 4 4 583 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 1 1 2 2 3 3 4 4 58' 92-13"0248 92'53 9258 9263 9269 9274 9279 9284 9289 1 l'2 2 S 3 4 4 5

85 929" 9299 9304 9309 9315 9320 9325 9380 9335 9340 1 1 2 2 8 3 4 4 586 9345 0350 9355 93GO 9365 9370 93'i5 9380 !la85 9390 1 ] 2 2 3 3 4 4 587 9395 0400 9405 9410 9415 9420 94.25 9430 9435 944'0 o 1 1 2 2 2 3 4 4.88 9445 9450 9455 9460 9465 9469 9474 9479 9484 94.89o 1 1,2 2 3 S .( ,89 9494 9499 9504 9509 9513 9518 9523 9528 95.33 9538 o 1 1 2 2 3 3 4 ,

90 9542 95479552' 9557 956,2 9566 9571 9576. 9581 9586 o 1 1 '2 2 S 3 , ,91 9590 9595 9600 9605 -96099614 9619 OG24 9628 9633 o 1 1 2 2 3 S 4 ,92 9638 0&43 9647 0652 9657 9661 9600 9671 9675 9680 o 1 1 2 2 S 8 4 493 9685 9689 9694 9699 ~703 9708 9713 9717 9722 9727 o 1 1 2 2 8 3 4. 4.94 9731 9736, 9741 9745 9750 9754 9759 9'163 9'168 9773 o 1 l' 2 2 3 8 4 4.

95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 o 1 1 2 2 S B , 4.96 9823 9827 9832 9836 9841 9845 9850 9854 9859. 9863 o 1. 1 2 2 3 8 4. 4.97 9868, 9872 9877 9881 9886 9890 98.9' 9899 9903 99ÓS O' tI 2 2 3 8 4 4.98 9912 9917 9921 9926 9930 9934 9989 9943 99~8 9952 o 1 1 2 2' S 8 la 4.99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 o 1 1 2 2 8 8 8 4.

N I O. 1 2 s 6 7 89 11 2 al' & 617 8 9

~

~

,-

Tabla11. Antiloga'r~tmos delosnúmeros

287

M o 1 2 3- 4 6 6 7 8 9 1 2 3 4 5- 6 8 9

.00 1000 1002 1005 1007 1009 1012 1014 1018 1019 1021o o 1 1 1 1 2 2 2-

.01

10.S '0'6 '0'8 lOS° lossros. 1038 1040 104' 104'

o o 1 1 -1 -1 2 2

.02 1047 1050 1052 1054 1057 1059 1062 1064 1067 -1069-o 0-1 1 1 1 2 2 2.

.03 1072 1074 1076 1079 1U81 1084 1086 1089 1091 1094 o o 1 1 1 1 2 2

.04 1096 1099 1102 1104 1107 1109 1112 114 1117 1119 o 1, 1 1. 1 2 :2-2 2

.05 1121125 1127 1130 1132 1135 1138 1140 1143 1146 011 112 2 .,

.06 1148 1151 1153 1156 1159 1161 1i64 1167 ,1169 1i72 011 112 f} " :3

.07 1175 1178 1180 183 1186 1189 1191 1194 1197 i199 011 112 2 2 2

08 1202 1205 1208 1211 13 1216 1219 1222 1225 1227 011 lIt 2 :!13

.09 1230 1233 1236 1239 124 1245 1247_1250 1253 1256 o 1 f 1.1 2 2 2 3

.10 1259 1262 1265 1265 1271 1274 127& 1279 1282 1286 o 1 1 1 i 2 2 2 3

.111288 1291 1294 1297 13001303 1306 1309 1312 1315 o 1 1 1 2;2 2 2 :}

.12

1318 1321 1324 i327 1330rla34 1337-1340 1343 1346

o 1 1 1 2 2 2 2. ..

.13 1349 1352 1355 1á58 1361 1365 1368 1371 1374 13?7 o 1 1 1 2 2 2 33

.14 1380 1384 1387 1390 1393 1396 1400 1403 406 1409 o 1 1 1 2 2. 2 3 3

-.151413 U16 1419 1422 142#)11429 14:12 135 1439 1442o 1 1 1 2 2 2 3 3

.161445 1449 1452 1455 14591462 1466 1469 1472 1476 o1 1 1 2. 2 2 3 3

.7 1479 1483 1486 1489 1493 149b 1500 1503 1507 1510 o 1 1 1 2 2 2 3 3

.181514 1517 1521 1524 1528 1431 1535 1588 1542 1545 o 11 1 2 2 ,2 3 3

.191549 15521556156015631567 1570 15741478 1581 o 1.1 1 2 2 3 3 3

.20 1585'1589 1592 1596 1600 1603 1607 1611 1614 1618 o 1 1 1 2 2 3 3 3

.21 1622 1626 1629 1633 167 1641 1644 -1648 1652 1656 o 1 1 2 2 2 3 3 3

.22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 o 1 1 2 2 2 3 '33

.231698 1702 1706 710 17t4 1718 1722 1726 -17301734 o 1 1 2 2 3 ,4

.24 1738 1742 1746 1750 -17541758 1762 1766 1770 1774 o 1 1 2 2, 2 3 4

.25 1778 1782 1786 1791 1795 1799 180318071811181e0_1 1 2 2 2 3 3 -4

.26 1820 lR24 1828 1832 1837 ]841 1845 1849 1854 185R o 1 1 2 2 S 3 3 4

.27 lR62 1866 1871 1875 1879 1884 1888 1892 189.71901'o 1 1 2 2 3 a 3 4

.28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 o 1 1 2 2 3- 3 4 4

.29 1950 954 1959 1963 968 1972 1977 1982 1986 1991 o 1 1 -2 2 8 3 4 4

.30 1995 2000 2004 009 2014 2018 2023 2028 2032 2087 011 2 2 8 3 ,4 4

.312042 2046 2051 2056 2061 2065 2070 2075 2080 2084 o 1 122 8 3 4 4

.322h89 2094 2099 2104 2109 2113 2118 2123 2128 2133 o 1 1 2 2 8 3 4 4

.33 213R- 2143 2148 2158 215R 2163 2168 2173 2178 2183 o 1 1 2 2 8 3 4 -4

.342188 2193 2198 2203 228 2213 2218 2223 2228 2234 1 1 2 2 3 8 445

.35 229 22442249225422592265 2270 2275 2280 2286 1 1 -2 2 3 8 445

.362291 2296 2301 2307 2312 2317 2323 -23282833 2839 1 1 2 2 8 8 4 4 5

.372344 2860 2355 2360 2366 271 2377 2382 2388 2393 1 f 2 2 3 S 4 4 5

.382399 2404 2410 2415 2421-2427 2432 2488 2443,2449 1 1 2 2 3 3 4 4 5

.392455 2460:2466 2472 2477 2483 2489 295 2500 2506 1, 1 2 2 3 8 4 5 5

.40 2512 2518 2523 2529 253 2541 2547 2553 2559 2564 1 1 2 2 á 4 4 5 5'

.41 270 2576 2582 2788 2594 260026062612 26182fi24 1 1 2 2 8 4- 4 5 5

.42 2630 2636 2642 2649 2655 2661 2667 2673 2679 268;:;-1 1 2 -2-3 4 4 5 6

.43 2602 2698 2704 2710 271R 272a 2729 2735 2742 274R 1 1 2 8 S 4- 4 5 6

.44 2754 2761 2767 2773 2780 2786 2793 2799 2805 -2812 '1 1 2 8 S 4 4. 5 6

.452R18 2825 B31 2838 284412851 2B58 2864 2871 2871 1

1 2 8 - S 4 5'5 6- .46 2RR4- 2891 2897 2904 2911 2917 2924 2931 2938 2944 1 1 2 8 S 4 5 5 6

.47 2951 2958 2965 2972 979 2985 2992 2999 8006 3013 1 1 2 8 S 4 5 5 6

.48 3020 3027 3034 3041 304R 055 3062 3069 3076 3083 1 1 2 8 4 4 5 6 6

.49 3090 3097 3105 3112 3119 3126 3133 3141 3148 8155 1 1 284...4- 5 6 6

Al o 1 2 3 4 -5 6 . 7 8 9 1 -2 3 456 7 8 9

288 '

Tabla11. Antilogaritmos de los números

Jl I ,o '4 5 6 7, 81 2 -3

.60 3162 3170 8177 3'184 3192

1

3199 3~06 3214 3221 322~ 1 2 2 8 " 4 5 6 'l.51, 3236 3243 8251 ,321)8 32M 3~73 3281 8289 3296 3304 1 2 2 3 4 1) :; 1) '1.52 3a,11 3319 332'1 3334 3342 3350 3357 88G6 8873 8381 1 2 3 SoiS 5 6 '1.63 3388 3396 3404 3412 3420 3428 3436 8"3 84~1 3459 1 2 2 I 4 5 6 6 't.64. 3467 84.76 34.83 3491 3499 35,08 3516 3524. 3532 8540 1 2 2 3 4. 5 6 6 't

.&6 3548' 3556 3565 3573 3581 3589 3597 3606 8614 8622 1 2 2 S " 50 6 '1 7

.56 3631 3639 3648 3656 36tH, ;¡'t>73 3681 3690 8898 8'107 1 2 8 3 4 5 () 7 8

.573715 4724 3733 3741 875U 3758 3767 37'16 8'18.& 3793 1 2 8 3 .1 5 6 '1 8

.58 3802 3811 3819 3828 3P37 3R46 3855 3864 8873 3M'2 1 2 3 " 4. 5 6 1 8

.59 a890 3899 3908 3917 a926t39~6 3945 3954 3963 9' 12;.1 2 S " Ó 1) 6 7 8

.60 8981 3990 3999 4009 (018 4027 4036 4046 4055 4064 ~ 2 3, 4 5 6 6 7 R

.61 4.074 4083 4093 4102 4111 4121 4130 4140 4150 .&159 1 2 3 4' 5 G 7 8 9

.62 3169 41.78 4188 4198,4207 4217 4227 4236 4246 4256 1 2 S .&5 6 7 8 9

.68 4.266 4276 4285 4295 4~e5 4315 4325 4335 454!>4351) 1 2 3 " 5 6 7 8 9;64 01365 4375 4385 4395 4406 4416 4426 4436 4446 4457 1 2 3 '4 5 6 78 9

.651

4467 4477 4487 449f1 4f10HI'H19 4529 4539 4550 4560 1 2 81

'~ 5 6 7 8 9'

.66 4571 45d1 4592 46Ú3 4.tiI.3;,4624. 4634 4645 .&656 4667 1 2 8 <. 5 6 7 910

.67

1

4677 46rll'Sc 46Y

..

9 4710 4721.-tn2 4H~.

i 4753476447'151 2 8\,

4.,5 7. 8 910.68 J.7!f6 4797 4'808 4819 4831 .1843 4853 4864 .&8754887 1 2 3 4. 6 7 8 910~6,9 4.~9~ "9u9 4no 4932 49 t3 11955 4.~66 4977 4989 5000 1 2 3 ¡ 5 6 ,7 8 9 10

.10 5012 5023 5035 5047 5(¡ ~ 5070 &Úb~ !¡093 5105 51171

t.

.11 51295140 5152 5164517ü~1ari 52uU~~1252246336132 ~248 5260 6272 5284 5297 5309

.

4:.

iZl 5333 5346 535~1

1

1

.73 531U fi3d3 5395 5408 5420513~ 544& 5458 5470 5483 1

.r45495 6508 5521 5534 554b ~5JD ~57¿ 55rl5 5598 561U 1

~5 5623 5636 564é 5662 5675 56d9 ~70~ 5715 5728 574111.76 5754 5768 '5781 579.~ 51<""

t5t121 58;}.10»4~ 5861 5875

1

1

~7 5888,5~0259~G5Y~35D4J.~~575970~~a4 &~9& 6012 t.78 6026 6U39 6053 6u6-, bU~j 16\J~5 (;u>V íi124. (;13i:1 6152

,1

'1

.79 6166 6180 6194 6209 622J 62~7 6252 6266 62~1 6295 1

.80 6310 6324 6339 6i53 6H6~ "JA3 ~S97 6412 6427 64~2 1

.81 6457 6411 6~86 6501 6516 1¡~Jlti5~6 6561 6577 ~5D2

1

¡2

.82 li607 6622 6637 665,3 (i(j(j~ GuS3 6699 6714. 6730 6745 2

.83 6761 6776 6792 6808 6823 tHI:19 6855 6871 6887 6'902 2

.84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 2

2 4 5 1:) 7 8 ,9 112 4 5 6 7 810112 4 5 6 7 910113 .. 5 6 8 910113 4 5 6 -,8 9 10, 12

3 , 5 7 8 0101:::341& 7 8 91112

S 41-5 7 8 10 11 12:\ ,4 '

1

(j 7 8 10 11 1334,6 7 ~ 101113

3 4

1

6' "1 .9 1(1 12 13:1 ' 5' 6 8 9 11 12 14S 5

1

6 8 9 11 12 143 5 6' 8 9 1l 13 14'3 5 6 8;1.0 1113 15 I \

.85 7079 7096 7112 7129 7145

1

7161.86 7244 7261 7278 7295 731.1 7328.87 7413 7430 7447 7464 74B2 ~499~8 7586 7603 7021 7638 7656 7674.89 7762 ~7~~ 7798 7816 7H34.7¿~~

7178 7194 7211 7228 2 3 5 7 ~ 107345 ,1362 7379 7396 2 3 5 1 8 lO'7516 7534 7551 '756H2 3 5 7 9107691 7709 7727 7745 2 4 5 7 9117670 7d,89 790"í 7925 2 -1 5 1 911'

1213 15121315- -

12 14 1612 U 1613 1416

.90 7943 '1962 '7980 7998 8017

1

1)035 8054 8072 8091 811012' ,¡ 6 7 91l 131517.91 81.28 8141 8166 8185 8204 8222' 8241 8260 8279 8299 2 4 6 8 911 131517'.92 8318 8337 8356 H375 8395 8414 8433 8453 8472 .849~ 2 4,6 81012 141517.93 8511 853185;}1 ~i'l570 S59f) ,¡HilO K630 8650 8(370 8690 ? 4. 6 B]O 12 141618.94 S710 8730 8750 8770 M790 !8h10 8331 8851 8872 88n 2 4. 6 8 1012 1-1161,8

.95 8913 8933 8954 H974 8!>!)51!íoJG 903'6,90519078 9099 2 4. 6. B 1012 '1517 19

.96 9120 9141 9162 '')683 9204 In~G !!247 9268 9290 9311 , 4. 6 ti 11 131

151719

.97 93~3 91;54 /),;76 9397 9.¡1!!!'.'1.,l1 !'.Hi2 U4M4 fj50'6 952112 4. 7 91113 151'120

.98 9550 9572 9594 9616 9íi3..1~¡(;6\ !j'-,>!;: n05 9727 9750 2 4. 7 91113 '16 18 ~O

~ .772 ~795 .'.17 9..0 '..31'''.. ~.o. "031 995{ 09771~,~.1'6 ,. 20j! o 1 2' 3 .!:) U 7 8 9 '11 2 31'4 5 ~I7 89

1JiIII8I_"-

Tabla 111.Valores de Funciones Trigonométricas

289

Grados Radianes Sen Tg Ctg Cos

0° 00' .0000 .0000 .0000 1.0000 1.5708 WOO'10' .0029 .0029 .0029 343.77 1.0000 1.567Q 50'20' .0058 .0058 .0058 . 171.89 1.0000 1.5650. W30' .0087 .0087 .0087 11-4.59 1.0000 1.5621 30'40' .0116 .0116 .0116 86.940 .9QQ9 1.6592 20'50' .0145 .0145 .0145 68.750 .QW9 1.6563 10'

1° 00' .0175 .0175 .0175 67.290 .gggs 1.6633 .'r.' 00'10' .0204 .0204 .0204 49.104 .HM 1.66CM 50'20' .0233 ' .0233 .0233 42.964 .Q997 1.6476 40'30' .0262 .0262 .0262 38.188 .GGG7 1.644& 30'40' .0291 .0291 .0291 34.368 .tm6 1.6417 20'50' .0320 .0320 . .0320 31.242 .WtJ6 1.6388 10'

2° 00' .0349 .0349 .0349 28.636 . .99H 1.636Q "0 00'10' .0378 .0378 .0378 26.432 .Q993 1.6330 50'20' .0407 .0407 .0407 24.M2 .9tKt2 1.6301 40'30' .0436 .0436 .0437 22.904 .99QO 1.5272 30'40' .0466 .(M65 .0466 . 21.470 .9989 1.6243 20'50' .0495 .0494 .0496 20.206 .H88 1.6213 10'

3° 00' .0624 .0623 .0624 19.081 ."86 1.61&& 17.00'10' .0653 .OM2 .0663 18.076 .9985 1.6165 60'20' .0682 .0681 .0682 17.169 ."83 1.6126 40'30' .0611 .0610 .0612 16.350 ."81 1.6097 30'40' .0640 .0640 .0641 16.606 ."SO 1.5068 20'50' .0669 .0669 .0670 14.924 ."78 1.6039 10'

..0 00' .0698 .0698 .06" 14.301 ."76 1.6010 86° 00'10' .0127 .0727 .0729 13.727 ."74 1.4981 60'20' .0756 .0756 .0768 13.197 .9971 1.4962 40'30' .0'lgb .0786 .0787 12.706 .Q969 1.4923 30'40' .0814 .0814 .0816 12.261 .Q967 1.4893 20'60' .0844 .0843 .0846 11.826 .Q964 1.4864 10'

5° 00' .0873 .0872 .0876 11.430 .Q962 1.4836 85° 00'10' .0902 .0901 .09(H 11.069 .9969 1.4806 60'20' .0931 :0929 .0934 10.712 .9967 1.4777 40'30' .0Q60 .0968 .0963 10.386 ."M

}.47.s30'

40' .0989 .0987 .0992 10.078 ."61 .4719 20'60' , .1018 .1016 .1022 9.7882 .9948 1.4690 10'

6°00' .1047 .1046 .\061 9.6144 .9946 1.4661 '''0 00'. 10' .1076 .1074 .1080 9.2663 .9942 1.4632 60'

20' .1106 .1103 .1110 9.0098 ."39 1.4603 40'30' .1134 .1132 .1l3Q 8.77tW ."36 1.4613 30'40' .11M .11tU .1169 8.6666 ."32 1.4644 20'50' .1193 .ligo .1198 8.3460 .9929 1.4616 10'

to 00' .1222 .i21Q .1228 8.1443 ."26 1.4486 838 00'10' .12'61 .1248 '.1267 7.9630 .H22 1.4467 60'20' .1280 :1216 .1287 7.7704 .9918 1.4428 40'30' .13OQ .1306 .1317 7.6968 .9914 1.43" 30'40' .1338 .1334 .1346 7.4287 ."11. 1.4370 20'60' .1367 .1363 .1376 7.2687 .9907 1.4341 10'

8° 00' .1396 .1392 .1406 7.11M .9903 1.4312 '2° 00'10' .1426 .1421 .1436 6.9682 .9899 1.4283 50'20' .14M .144Q .1466 6.8269 .UtN 1.4264 40'30' .1484 .1478 .1496 6.6912 .9890. 1.4224 30'40' .1613 .1607 .1524 8.6606 .N86 1.4196 20'50' .1642 .1636 .1664 8.4348 .9881 1.4186 10'

,. 00' .1671 .1564 .1684 6.3138 .un 1.4137 81° 00'Cos Ctg Tg Sen Radianes Grados

290

Tabla 111.'Valores de Funciones Trigonométricas

Grados IRadianesl Sen Tg Ctg Cos1--

9" 00'10'

.1571

.16001.41371.4108

81° 00'50'

.1564 .

.1593.15/W.1614

6.31386.1970

.9877

.987220' .1629 .1622 .1644 6.0844 .9868 1.401\1 40' :30' .1658 .1650 .1673 6.9758 .9863 1.4050 30'40' .1687 .1679 .1703 5.8708 .9858 1.4021 20'60' .1716 .1708 .1733 6.7694 .9853 1.3992 10'

.10° 00' .1746 - .1736 .1763 6.6713 .9848 1.3963 80° 00'10' .1774 .1765 .1793 6.5764 .9843 1.39:W 50'20' .1804 .1794 .1823 6.4845 .9838 1.3904 40'30' .1833 .1822 .1853 5.3955 .9833 1.3876 30'40' .1862 I .1'851 .1883 5.3093 .9827 1.3846 20'50' .1891 .1880 . .1914 5.2257 .9822 1.3817 10'

11° 00' .1920 .1908 .1944 6.1446 .9816 1 3788 79° 00'10' 1949 .1937 .1974 6.0658 .9811 1.3759 50'20' .J97K .1965 .2004 4.9894 .9805 1.3730 40'30' .2007 .1994 .2035 4.9152 .9799 1.3701 30'40' .2036 .2022 .2065 4.8430 .9793 1.3672 20'50' .2066 .2061 .2095 4.7729 .9787 1.3643 10'

17° 00' . .2079 .2126 4.7046 .9781 1.3614 78° 00'10' - .2123 .2108 .2166 4.6382 .9775 1.3584 50'20' .2163 .2136 .2186 4.6736 .9769 1.3555 40'30' .2182 .2164 .2217 4.5107 .9763 1.3526 30'40' .2211 .2193 .2247 4.4494 .9767 1.3497 20'60' .2240 .2221 .2278 4.3897 .9750 1.3468 10'

I

I

13° 00' .2269 .2260 .2309

I

4.3316 .9744 1.3439 77° 00'10' .2298 .2278 .2339- 4.2747 .9737 1.3410 SO'20' .2327 .2306 I .2370 ".2193 .973l1 1.3381 40'30' .2366 I .2334 .2401 4.1653 .9724 1 3352 30'40' I .2385 .2363

I

.2432 4.1126 9717 1.3323 20'60' .2414 .2391 .2462 4.0611 .9710 1.3294 10'

14° 00' .2443 .2419 .2493 4.0108 .9703 1.3265 76° 00'10' .2473 .2447 . .2524 3.9617 .969.6 {.32a5 50"20' .2602 .24i6 .2655 3.9136 .9689 1.;i206 40'

I 30' .2631 .2604 .2586 3.8667 .9681 1.3177 30'

I 40' .2560 .2532 .2617 3.8208 .9674 l.J 148 20'

l.

60' .2589 2560 .2648 3.7760 .9667 13119 10'

15° 00' .2618 .2588 .2679 a.7.32 ..9659 1.3090 75° 00', 10' .2647 .2616 .2711 3.6891 .96b2 lo3Of.1 50'

20' .2676 .2M4 .2742 3.6470 .9644 ! 1.3032 40'30' .2705 .:..'f\7;¿ .2773 3.6069 .9t3ó \.3003 30'

40' ¡ .27:W

.:.?700 .2805 3.5666 .962!:' '.:';974 20'W .2763 .2728 .2836 3.5261 .9621 1.2945 10'

16° 00' I .2793 .2766 .2867 3..874 . .961J :'2915 74u OO10' , .2822 .2184 .2899 3.4495 .9605 1.2886 5(}'20' .2851 .2R12 .2931 3.4124 .9596 1.2867 40'30' .2880 .2840 .2962 3.3759 .958 1.2828 30'40' .2909 . .Z868 .2994 3.3402 .9580 1.2799 20'50' .2968 B96 .3026 3.3052 .952 J .2770 10'

11" 00' I

.2967 2924 .3057 3.2709 .9563 1.2741 73" 00'10' .2996 2952 .3089 3.2371 .9.')55 1.2712 60'20' .3025 .2979 .3121 3.2041 .9546 1 2683 40'30' .3054 .:1007 .3153 3.1716 .9537 1.26.')4 30'.0' .3Ó83 .;035 .3185 3.1397 .9528 1.2625 20'50' .3113 .3002 .3217 3.1084 .9520 1.2595 10'

11° 00' :t142 3090 3249 3.G777 .9511 1.2566 72° 00'--.- -- --.--------- -- -Cos Ctg Tg Sen Radianes Grados

Tabla 111.Valores de Funciones Trigonométricas

291

Grados IRadianesl Sen I fg

18° 00' .3142 .3090 .32-i010' .3171 .3118 .328120' .3200 .3146 .331430' .3220 .3173 .334640' .32M .3201 .337860' .3287 .3228 .M11

19" 00' .3316 .3266 .3«310' .3345 .3283 .M7620' .3374 .3311 .360830' .M03 .3338 .354140' .M32 .3366 .367460' .M62 .3303 .3607

20° 00' .M01 .3420 .3MO10' .3620 .3448 .367320' .3549 .M76 .370630' ,.3578 .3502 .3730.0' .3607 .3529 .377260' .3636 .3567 .380b

21° 00' .3666 .3584 .383010' .3694 .3611 .387220' .3723 .3638 .3006

,30' .3762 .3665 .3930'.0' .3782 .3692 .3073

60' .381.1 .3719 ..006

22° 00' .38f0 .37.6 .404010' .38&9 .3773 .407420' .3898 .3800 .410830' .3927 r .3827 .41.240' .396 I .J8:K

I"176

60' ;9' .8 4210

23° 00' .4014

I

.3907

I

.424610' .4M3 .39M .427920' .( "'7 ,:!N), .43143(V .4102

I

.987 I ,4M84u' I ',OJA- "38.50' .4160 ...o.t !

I,,"17

24° 00' .4180 .4067

I

.«6210' .4218 .4094 .148720' .4,2'i7 ..120 .452230' ..216 ..141

I

..55740' .4306 .4173 ..59250' .4334 .4200

I

.4628

25° 00' .4363 .4226 .466310' .4302 '..263 .469920' .«22 ..279

I

..7M30' .«61 .4306 .417040' ,«80 .4331

l..4806

50' .4509 ,358 .48f126° 00' .4638 .43806 I .4877

10' .-4667 ....10 I ..91320' .4,'>9'} .«36 I .495030' 4615 .«62

I

.498640' .46..'>4 .4488 .1>02250' ..683 .45a ,5059

27° 00'

:.!-. .454 )--'-':5095Cos Ctg

13.0177 .96113.0475' .96023.0178 .94022.9881 .94832.9600 .94142.931Q .9466

2.0042 .94662.8170 .94462.8602 .94362.8230 .9Ma62.7980 ."1'7,2.7725 .9401

2.7475 .93912.7228 .93872.6985 .93772.6746 .93672.6511 .935fi2;6279 .9M6

2.6051 .OaM2.6826 .93252.6605 .03162.6386 .93042.6112 .92032.4960 .9283

I 2.4751 .9212

I

2.4645 .92612.4342 .92602.4142 .92392.3946 .9228

I 2.3750 .921

I

2.3bb¡} .92062.3369 .91942.3183 .9182

I 2.2998 .9171I 2, ?J;¡,17 .9159

;¿.();,' .9141

2.2-i60 .91362.2286 .912-i2.2113 .91122.1943 .91002.1775 .90882.1609 .9076

2.1«5 ,.90632.1283 .12.1123 .90382.0066 .90262.0809 .90132.0666 .9001

2.0503 .89882.0363 .89762.02(}\ .89622.0057 .89491.9912 .89361.9768 .8923

1.9626 .8910

Tg Sen

'-

1.2666 72° 00'1.2637 60'1.2508 40'1.2-i70 30'1.2-i50 20'1.2-i21 10'

1.2392 11° 00'1.2363 60'1.2334 40'1.2306' 30' '

1.2276 20' .1.22-i6 10'

1.2217 100 00'1.2188 60'1.2160 40'1.2130 30' '1.2101 20'1.2072 10'

1.2043 69"00'1.2014 50'1.1986 40'1.1966 30'1.1926 20'1.1897 10'

1.1868 6'° 00''1.1839 60'1.1810 40'1.1781 30'1.1752 20'1.1723 10'

l.H. ' 67"(10'1.1665 50'1.1636 40'1.1606 30'1.1577 20'. .1"1-p. . 10'

1.1519 66° 00'1.1490 50'1.1461 40'1.1,(32 30'1.1403 20'1.1374 10'

1.1345 65° 00'1.1316 50'1.1286 40'1.1257 30'1.1228 20'1.1199 10'

1.1170 64° 00':1.1141 50'1.11: 2 40'1.1083 30'1.1064 20'1.1025 O'

1.0996 63° 00'

Radianes Grados

292

Tabla111.Valoresde FuncionesTrigonométricas

Grados Radianes Sen Tg Ctg Cos

27800' .4712 . .&091 1.9626 .8910 1.0996. 63° 00'10' .4741 .46e8 .6132 I.M86 .8897 1.0966 60'20' .4771 .4692 .6169 1.9347 .88M 1.0937 W30' .dOO ..e17 .6206 1.9210 .8870 1.0908 30'W .4829 .4M3 .63 I.DOn .8867 1.0879 20'60' .4868 . .6280 1.8MO .8M3 1.0860 10'

2'° 00' .4887 .4696 .6317 1.8807 .8829 1.0821 62° 00'10' .4'16 .4720 .63M 1.8676 .8816 1.0792 60'20' .4N6 .4746 .6392 1.8M6 .8802 1.0763 40'30' .4974 .

;le.M30 I.MI8 .8788 1.0734 30'

W .6003 .6.e7 1.8291 .8774 1.0706 20'60' .6032 .6606 1.8166 .8760 1.0676 10'g.,

2fO 00' .1081 .dü .6M3 1.8CHO .8746 I.OM7 61° 00'10' .1091 .4S74 .6681 1.7917 .8732 1.0617 60'20' .6120 ,.4899 .Ml' 1.7796 .8718 1.0688 W30' .614' ;.,C .6868 L7676 .8704 1.0669 30'W .6178 .6698 1.7668 .8689 1.0630 20'60' .6207 .6736 1.7437 .8676 1.0601 10'

34)800' .6238 .6774 t.7321 .8660 1.0472 60° 00'10' .6286 .6812 1.7206 .8646 1.0443 60'20' .62M .6060 .6861 1.7090 .8631 1.0414 W30' .6323 .6076 .6810 1.6977 .8616 1.038& 30"W .6362 .6100 .6930 1.6864 .8601 1.0366 20'60' .6381 .6126 .6969 1.6763 .8687' 1.0327 10'

31° 00' .MIl .6160 .6009 1.6M3 .8672 1.0297 '9° 00'10' .6440 .6176 .6048 1.6634 .8667 1-1)268 60'20' .6.ü9 .6200 .6088 I.M26 .8M2 1.0239 40'30' .M. .6226 .8128 1.6319 .8626 1.0210 30'W .6627 .6260 .81es 1.6212 .8611 1.01S1 20'60' .6666 .6276 .8208 1.6107 .M96 1.0162 10'

32- 00' .6686 .6299 .8249 1.6003 .MSO 1.0123 5'° 00'10' .M14 .13 .8289 1.6100 .M66 1.0094 60'20' .6M3 .6348 .8330 1.6798 .M60 1.0066 W30' .6672 .6373 .6371 1.6697 .M34 1.0036 30'W .6701 .13. .M12 1.6617 .MiS 1.0007 20'60' .6730 .1422 .MIS I.M97 .M03 .1977 10'

33° 00' .6780 . .MM 1.1399 .8387 . .9M8 57° 00'10' .67S9 .M71 .6638 1.6301 .8371 .1919 60'

I 20' .681S .MII .8677 1.6204 .8366 .9890 W30' .IM7 .6619 .8819 1.6108 .8339 .9861 30'W .6876 .6144 .8881 1.6013 .8323, .9832 20'60' .6106 .6688 .8703 1.4919 .8307 .9803 10'

34° 00' .61M .6692 .6746 1.4826 ' .8290 .9774 56° 00'10' .6963 .6618 .6787 1.4733 .S274 .9746 60'20' .6992 .6640 .6830 1.4Ml .S268 .9716 40'30' .80:n .I6M .6873 1.4660 .8241 .9887 30'40' .8060 .6688 .6916 1.4480 .8226 .9667 20'60' .8080 .6712 .6169 1.4370 .8208 .9628 10'

WOO' .8109 .6738 .7002 1.4281 .8192 .9699 55° 00'10' .8138 .6760 .7048 1.4193 .8176 .9670 60'20' .8187 .6783 .7089 1.4106 .8168 .9Ml W30' .8111 .6807 ..7133 1.401' .8141 .9612 30'W .8226 .6831 .7177 1.3934 .S124 M83 20'60' .82M .I8M .7221 1. .8107 .MM 10'

36° OCY. .8283 .687S .7266 1.37M .8090 .M26 5.° 00'

Cos Ctg Tg Sen Radianes Grados

Tabla 111.Valores de Funciones l)igonométricas

293

Grados Radianes Sen Tg Ctg Cos

3'° 00' .6283 .5878 .7265 1.3764 .8090 ' .9425 5... 00'lO' .6312 .5901 . .7310 1.3680 .8073 .9396 60'20' .63-41 .5925 .73M 1.3597 .805e .9367 40'30' .6370 .5948 .7400 1.3514 .8039 .9338 30'W .&400 .6972 .7446 1.3432 .8021 .9308 20'W .6429 .5995 .7490 ' 1.3351 .8004 .9279 10'

37° 00' .6468 .6018 .7636 1.3270 .7986 .9250 ' 53. 00'10' .6487 .6041 .7681 1.3190 .7969 .9221 60'20' .6516 .6065 .7627 1.3111 .7951 .9192 40'30' .6M5 .6088 .7673 1.3032

BI.9163 - 30'

40' .6574. .6111 .7720 1.2164 .9134 20'60' .6603 .61M .7766 1.2878 .7898 .9106 10'

3'° 00' .6632 .6157 .'7813 1.2798' .7880 .9076 52° 00'10' .6661 .6180 .7860 1.2723 .7862 .9<M7 50'20' .6690 .6202 .7907 1.2647 .7844 .9018 40'30' .6720 .6225 .79M 1.2572 .7826 .8988 30'40- .6749 .6248 .8002 1.2497 : .8959 20'50' .6778 .6271 .8060 1.2423 .8930 10'

39° 00' .6807 .6293 .8098 1.2349 : .8901 51° 00'10' .6836 ;6316 .8146 1.2276 .8872 50'20' .6865 .6338 .8196 1.2203 .7735 .883 40'30' .6894 .6361 .8243 1.2131 .7716 I .8814 30'40' .6923 .6383 .8292 1.2069 .7698 .8785 20'50' .6952 .6406 .8342 1.1988 .7679 .8756 10'

.0° 00' .6981 .8428 .8391 1.1918 .7660 .8727 SOo00'10' .7010 .6450 .8441 1.1847 .7642 .8698 50'20' .7039 .6472 .8491 1.1778 .7623 .8668 40-30' .7069 .6494 .&MI 1.1708 .7604 .8639 30'40- .7098 .6517 .8691 1.1640 .7686 .8610 20'50' .7127 .6639 .8642 1.1571 .7566 .8581 10'

.1 ° 00' .7156 .6561 .8693 1.15CM .7M7 .8552 .,. 00'10' .7185 .6583 .8744 1'.1436 .7528 .8523 50'20' .7214 .6604 .8796 1.1369 .7509 .8494 40'30' .7243 .6626 .8847 1.1303 .7490 .8465 30'40' .7272 .6648 .8899 1.1237 .7470 .8436 20'50' .7301 .6670 .8962 1.1171 .7451 .8407 1

.2° 00' .7330 .6691 .9O(K 1.1106 .7431 .8378 .'0 00'10' .7369 .6713 .9057 1.1041 .7412 .8348 50'20' .7389 .6734 .9110 1.0977 .7392 .8319 40'30' . .7418 .8766 .9163 1.0913 .7373 .8290 30'40' .7447 .8777 .9217 1.0850 .7353 .8261 20'60' .7476 .8798 .9271 1.0786 .7333 .8232 10'

0° 00' .7506 .6820 .9325 1.0724I

,.7314 .8203 .7° 00'10' .7534 .6841 .9380 1.0661 .7294 .8174 60'20' .7563 .6862 .9435 1.0698 .7274 .8145 40'30' .7692 .6884 .9490 1.0638 .72M .8116 30'40- .7621 .6905 .9646 1.0477 .7234 .8087 20'50' .7660 .8926 .9601 1.0410 .7214 .8058 10'

.... 00' .7679 .6947 .9857 1.0366 .7193 .8029 4'. 00'10' .7709 .6967 .9713 1.0296 .7173 .7999 . 50'20' .7738 .6988 .9770 1.0236 .7163 .7970 40-30' .7767 .7009 .9827 1.0176 .7133 .7941 30'40' .7796 .7030 .9884 1.0117 .7112 '.7912 20'50' .7826 ,.7060 .9942 1.0068 .7092 .7883 10'

..s. 00' .78M .7071 1.0000 1.0000 .7071 .78M .5° 00'

Cos Ctg Tg Sen Radianes Grados

294

. TablaIV. logaritmosde FuncionesTrig1)npmétncas

Grados Log Sen, Log Tg Log Ctg Log Cos

0° 00'2'.6363

90-00'10' .4637-3 .4637-3 .0000 60'20' .7M8-3 .7M8-3 2.2362 .()()()(). tO'30' tK08- 3 .9409- 3 2.06tn .0000 lO'<10' .0658- 2 .Ó658- 2 1.9M2 .0000 20'60' .127 2 .1627-2 1.8373 .0000 10'

JOOO' I .2419.-.2 .24H -2 1.7681 .9H9-1 ,.. 00'10' .3088 - 2 .3089 - 2 1.6911 .9999-1 60'20' .3668 2 .3669 -2 1.6331 .9999-1 .0"30' .U792 .4181-2. . I.68U .9999-1 30'40' .4637 2 .4638-2 1.6362 .9998-1 20'60' .6060 "':-2 .6063 -2 1.4tH7 .ms -'1 10'

2°00' .6428-:-2 .M31 -2 1.466G .9997-1 ... 00'10' .6776-2 .6779 2 1.4221 .9997 - 1 '60'20' .6097'...,..2 .6101-1 1.3899 .9996 -1 tO'30' .6397 ":-2 .MOl -2 1.3699 .9996 -1 30'40' .6677 ".-2 .6682 -2 1.3318 .9996 -1 20'60' -.6NO,,:-2 .6946-2 1.3OM .9996 -1 10'

3° 00' .7188'":-2 .7194-2 1. .9994-1 Ir 00'10' ' .74232 .7429-2 1.2671 .9993 -1 60'20' .7&&5-2 .7662-2 1.2348 .9993-1 .o'lO' .7857- 2 .7866-2 1.2136 .9992-1 3Ó'40- .8069 :..,-2 .8067 2' 1.1933 .99tH-1 20'60' .8261 - .8261-2 1.1739 .9990-1 10'

4°00' .8436 - 2 .8ü6 -2 1.16M .9989-1 N. 00'10' .8613-2 .8624 -2 1:1376 .9989-1 60'20' .8783-2 .8796- 2' 1.1206 .W88 -1 40'30' .8946- 2 .8960- 2 1.1040 .9981-1 lO'40' .9104 -2 ' .9118-2 1.0882 .9986-1 20'60' .9266'-2 .9212-Q 1.0728 ;9985-1 10'

'000' .9403-2 .9420-2 1.0680 .9983 -1 '5" 00'10' .9646- 2 .9663-2 1.0437 .9982 -1 60''20' .9682-2 .9701-2 1.0299 .9981 -1 40'30' .9816 -2 .9836-2 1.01M .9980 -1

I

30'40' .9946 -2 .9066- 2 1.00M .

.9979-.:1 20'60' .0010-1 .0093-1 .9901 .9971 -1 10'6°00' .0192-1 .0216...1 .9184 .9976-1 84° 00'10' 0311 -1 .0336-.1 .96&& .9976-1 60'20' .0426- 1 .0463-1 .9M7 .9973'-1 <10'30' .0639-1 .0567-1

t.9433 .9972-1 lO'40' .0648 -1 ,0678-1 .9'1.2 .9971 -1 20'60' .0766 -1 0786 1

I

" '1.1 .9969-1 10'r 00' .0869 -1" .0891-1 .9 \ 0'9 .991'8 -1 '3° 00'

10' '0961 -1 .0996- 1 .9005 .9ff8t- 1 60'20' .1060-1 .1096 ....1 S .V.1f\..; - 1 40'30' .1157-1 .11941 .Slma .9963 -1 3O40' .1262 -1 .121H -1 .870G .9961 -1 20'60' .1346 -1 .1386 -1 .8615 .99'69-1 10''0 00' .1436 -1 .1478 -1 .8f>22 9958-1 828 00'10' .1525 -1 .1669-1 .8431 .9956 -1 60'20' .1612-1 .1658-1 .8342 .99&4 -1

I

40-30' .1697 1 .1745 -1 .8256 .9952 -1 30'40' .1781 -1 .18J} -1 .8H9 .0050 -l 20'60' 1863 - 1 .1915..11 .8086 .0048 -1 10'- .1943 -1 .1997 -1 .8003 .994:> -1

I IJo COI'. -

Log Cos Log . Ctg Log Tg Log Ser. I Grauos

Tabla IV. Logaritmos de Funciones TrigotlOmétricas

Grados Log Seo Log Tg Log Ctg Log Cos--

9° 00' .1943 - 1 .1997 -1 .8003, .9946 - 1 81° 00'10' .202 - l' .2078 -1 ,7922 .9944 -1 50'20' .2100 1 I .2158 - 1 .7842 .9942 -1 40'30' .2176-1 I .2236- 1 .7764 .9940 -1 30'40' .2251 - 1 i .2313 - 1 .7687 .9938 -1 20'50' .2324 - 1

I

.2389 - 1 .7611 .9936 -1 10'

10°00" .2397 - 1 .2463 - 1 .7537 .9934 -1 $0° .00'10' .2468 - 1 .2536 - 1 .7464 .9931 -1 50'20' .2538.-1 ¡ .2609- 1 .7391 .9929 -1 40'30' .2606 - 1 .2680-1 .7320 .9927'-'- 1 30"40' .2674 -1 .2750 -} .7250 9924 - 1 20'50' .2740 -1 .2819 - 1 .7181 .9922 -1 10'

11° 00' .2806 - 1 .2887 -1 .7113 .9919 -1 . 79° 00'10' .2870 -1 .2953 -1 .7047 .9917-1 50'

g: I

.2934 - 1 .3020 - 1 .6980 .9914 -1 40'

.2997 - 1I

.3085 - 1 .6915 .-9912-1 30'40' .3058 1 .3149 -1 .6851 .9909 -1 20'50' .3119-1

I

.3212-1.- .6788 .9907 -1 10'

I2° 00' .3171J-l .3275 -1 .6725 .9904 -1 78° 00'10' .3238 - 1 .3336 - 1 .6664 .9901 -1 50'20' .3296 - 1 .3397 -1 .6603 .9899 - 1 40'30' .3353 - 1 .3458 - 1 .6542 .9896 -1 30'40' .341U -1 .3517 -1 .6483 .9893 - 1 20'50' .3466 - 1 .3576 - 1 .6424 .9890 -1 lO'

13° 00' .3521 -1 .3634 .J 1 .6366 .9887 -1 77° 00'10' I .3575 - 1 .3691 - 1 . .6309 .9884 -1 50'

20' I .3629 - 1 .3748 - 1 .6252 .9881 -1 40'30' I .3682 - 1 .3804 -1 .6196 .9878 -1 30'40' .3734 - 1 .3859 -1 .6141 .9875 -1 20'

50' r.786 - 1 .3914 -1 .6086' .9872 -1 10'

1..° 00' I

.3837 - 1 .3968 - 1 .6032 .9869 -1 76° 00'10' .3887 - 1 4021 - 1 .5979 .9866 -1 50'20' .3937 - 1 4074 - 1 .5926 .9863 -1 40'

30' J .3986 - 1

I

.4127 1 .5'873 .9859- 1 30'40' .4035. - i .4178 -1 .5822 .9856 -1 20'50' .4083 - 1 .4230- 1 .5770 .9853 -1 10'

I5° 00' .4130 - 1

I

.4281-1 .5719 .9849-1 '75° (,J'10' .4177-1 .4331-1 .5669 .9846 - 1 50'20' .4223 - 1 .4381-1 .5619 .9843 -1 40'30' .4269- 1 .4430 - 1 .5:?70 .9839-1 30'40' I . .4314-1 .4479 1 ..5521 .9836 -1 20'50' ¡ .4359-1 .427 - 1 .5473 .9832 -1 10'

16° 00' .4403- 1 .4575-1 .5425 .9828 -1 74° 00'10' .4447-1 .4622-1 .5378 .9825 -1 50'20' .4491-1 . .4669-1 .5331 .9821 -1 .40'30' -4533- 1 I .4716 -1 .5284 .9817 -1 30'40' .4576 - 1 .4762 -1 .5238 .9814 -1 20'50' .4618-1 I .4808 - 1 I .5192 .9810 -1 10'

17° 00' .4G59 - 1I

.4853 - 1.1

.5147 .9806 -1 73° 1)0'10' .470l1 - 1 .4898- 1 .5102 .9802 - 1 . 50'20' .4741 -' I .4943 - 1

I

.5057 .9798 - 1 40'30' I 47 1- 1

I

.4987- 1 .5013 .9794 -1 30'40' 1 .4821-1 .5031 - 1

I

.4969 .9790 -1 20'50' ¡ .48G1 - 1 ! .5075 - 1 .4925 .9786 -1 10'

I

I

18° 00' 1-- .4900 - 1 I- .5118 - 1 .4882 .9782 -1 72° 00'--l ¡ Log 3 !ogCtg Log Tg Log Sen Grados

295

296

I

Tabla IV. logaritmos de Funciones Trigonométrica's

Grados Log Sen Log Tg Log Ctg Log Cos

18° 00' .4900-1 .5118-1 .4882 .9782-1 72° 00'10' .4939-1 .5161-1 .4839 .9778-1 50'20' .4977-1 .5203 - ] .4797 .9774-1 40' '30' .6015-1 .5245-1 .4755 .9770-1 30'40' .6052-1 .5287-1 .4713 .9765-1 20'50' .6OVO-1 .29 -1 .4671 .9761 -] 10'

1,. 00' .5126-1 .5370-1 .4630 .9757-1 71° 00'10' .5163-1 .5411-1 .4589 .9152 -1 50'20' .5199-1 ' .5451-1 .4549 .9748 -1 40'30' .5235-1 .5491-1 .4509 .9743-1 '30'40' .5270-1 .6531-.1 .4469 .9739-1 20'50' .5306-1 .5571-1 .4429 .9734-1 10'

20° 00' .5341-1 .5611-\ . .4389 .9730-1 70000'10' .5375-1 .5650-1 .4360 .9725-1 50'20' .5409-1 .5689-1 .4311 .9721-1 40'30' . .5443-1 .5727-1 .4273 .9716-1 30'40' .5477-1 .5766-1 .4234 .9711-1 20'60' .6510-1 .5804-1 .-&196 .9706-1 10'

21° 00' .5543-1 .6M2 - 1 .4168 .9702 - 1 6,. .00'10' .5576-1 .5879-1 .4121 . .9697-1 60'20' .5609-1 .5917-1 .4083 .9692-1 40'30' .5641-1 .5954-1 .4046 .9687-1 30'40' .5673-1 .5991-1 .4009 .9682-1 20'50' .5704 -1 .6028- 1 .3972 .9677-1 10'

22° 00' .5736-1 .60&(-1 .3936 .9672-1 68° 00'10' .5767-1 ' .6100 -1 .3900 .9667 -1 50'20' .5798-1 .6136-1 ' .3864 .9661-1 40'30' .5828-1 .6172-1 .3828 .9656-1 30'40' ' .6859-1 .6208-1 .3792 .9651-1 20'50' .5889-1 .6243-1 .3757 .9646-1 10'

23° 00' .5919-1 .6279-1 .3721 .9640-1 67° 00'10' .5948-1 .6314-1 .3686 .9635'-1 50'20' .5978-1 .6348-1 .3652 .9629- \ 40'30' .6007 1 .6383-1 .3617 .9624-1 30'40' .6036 -1 .6417-1 .3583 .9618-1 20'50' .6065-1 .6452-1 .3548 .9613-1 10'

2"° 00' .6093-1 .6486-1 .3514 .9607-1 66° 00'10' .6121-1 .6520-1 .3480 ..9602- 1 50'20' .6149-1 .6553-1 .3447 .9596-1 40'30' .6177-1 .6587 -1 .3413 .9590 -1 30'40' .6205-1 .6620- 1 .3380 .9684-1 20'50' .6232-1 .6654-1 .3346 .9579-1 10'

25° 00' .6259-1 .6687 -1 .3313 .9573-1 65° 00'10' .6286-1 .6720-1 .3280 .9567-1 50'20' .6313-1 .6752 -1 .3248 .9561-1 40'30' .6340-1 .6785 -1 .3215 .9555-1 30'40' .6366-1 .6817-1 .3183 .9649- 1 20'50' .6392-1 .6850- 1 .3150 :9543-1 10'

26° 00' .6418-1 .6882-1 .3118 .9537-1 64° 00'10' .6444-1 .6914-1 .3086 .9530-l. 50'20' .6470 -1 .6946 -1 .3064 .9524-1, 40'30' .6495-1 .6977-1 .3023 .9518-1 ' 30'40' .!}52l-1 .7009-1 .2991 .9512 - 1 20'50' .6546 -1 ,.704()'-1 .296<1 .9505-1 10'

27° 00' .6570-1 .7072-1 .2928 .9499-1 63° 00'

Log Cos Log Ctg Log Tg Log Sen Grados

297

Tabla IV. lógaritmos de Funciones Trigonométricas

Grados Log Sen Log Tg

I

Log Ctg I Log Cos--21° 00' .6670-1 .7072-1 .2928 .9499-1 63° 00'

10' .6595-1 .7103-1 .2897 .9492-1 60'20' .6620-1 .7134-1 .2866 .9486-1 40'30' .6644-1 .7165-1 .2835 .9479 -1 30'40' .6668-1 .7\96-1 .2804 .9473-1 20'50' .6692-1 .726 -1 .2774 .9466-1 10'

28° 00' .6716-1 .t57-1 .2743 .9459-1 2° 00' .10' .6740-1 .7.!87-1 .2713 .9453-1 50'20' .6763-1 .7317-1 .2683 .9-«6- 40'30' .6787-1 .7348-1 .2652 .9439-1 30'40' .6810-1 .378 -1 .2622 .9432-1 I 20'50' .6833-1 .7408-1 .2592 '.9425 -1 10'

29"00' .6866- 1 .7438-1 .2562 .9418-1 61o 00'10' .6878-1 .7467-1 .2533 .9411-1 50'20' .6901-1 .7497-1 .2603 .9404 -1 40'30' .6923-1 .7526-1 .2<674 .9397 -1 30'40' .6946-1 .7566-1 , .2444 .9390-1 20'50' .6968-1 ,7685-1 .2<616 .9383-1 10'

30° 00' .6990- 1 .7614-1 .2386 .9375-1 60000'10' .7012-1 .7644-1 .2356 .9368-1 50'20' .7033-1 .7673-1 .2327 .9361-1 40'30' .7055-1 .7701-1 .2299 .9353 -.1 30'40' .7076-1 .7730-1 .2270 .9346 -1 zo,.50' .7097-1 .7759-1 .2241 .9338 -1 10'

31>00' .7118-1 .7788--1 .2212 .9331 -1 9° 00'¡O' .7139-1 .7816-1 .21M JI323--1 50'20' .7160-1 .7845-'1 .2155 .9315 - J 40'30' .7181-1 .7873 -1 .2127 .9308-1 30'40' .72(H-1 .7902-1 .2098 .9300 -1 20'50' .72':2 -1 .7930- i .2070 .9292 -1 10' ,

32° 00' .7242 -1 .7958-1 .2<K2 .9284-. t 58° 00'10' .7262-1 .7986-1 .2014 .9276.- 1 50'20' .7282-1 .8014-1 .lv86 .9268 .- 1 40'30' .7302-1 .8042-1 .1958 .9260 -1 30'40' .7322-1 .8070-1 .1930 .9252-1 20'50' .7342-1 .8097- 1 .1003 .9244-1 1'

33° 00' . .73fH- 1 .8126-1 .1876 .9236-1 STo00'10' .7380-1 .8153'-1 .IM7 .9228-1 5Q'20' .7400-1 .8180-1 .1820 .9219-1 40'30' .7419-1 .8208-1 .J792 .9211-1 30'40' .7438-1 .8235- 1 .1765 , .9203-1 20'50' .7457-1 .8263-1 .1737 .9194-1 19'

34° M' .7476-1 .8290-1 r .1710 .9186-1 56° 00'10' .7494-1 .8317-1 .1683 .9177-1 50'20' .7513-1 .8344-1 .1656 .9169-1 ¡

40'30' .7531-1 .8371 -1 .1629 .9160 -1 30' í

40' .7550 -1 .8398-1 .1602 .9151 -1 20'50' .7568 -1 .s.&25-1 .1575 .9142 -.1 10'

35° 00' .7586 -1 .s.&52-1 1648 .9134 -1 .55900'10' .7604 -1 .8479 -1 .152i .9125 -1 50'20' .7622 -1 .8506 -1 .1494 .9116 -1 40'30' .7640-1 .8533-1 .1467 .9107-1 30'40' .7657-1 .8559 -'1 .1441 .9098 -1 20'50' .7675 -1 .8586-1 .1414 .9089 - t 10'

360 00' .192 -1

I

.8613-1

I

.1387 .9080- t .54° 00'

Log Cos Log . Ctg Log Tg Lag Sen Grados-- .----'

2U8

TablaIV. Logaritmo'sde FuncionesTrigonométricas

Grados Log Sen L()g Tg Log Ctg Log Cos- _.-36° 00' .7692-1 .8613-1 .1387 .9080 -1 5"° 00'

10' .7710 -1 .8639-1 .1361 .9070 -1 60'20' .7727 -1 .8666- 1 .13:H .9061-1 40'30' .7744-1 .8692-1 .1308 .9052 -1 30'40' .7761 -1 .8718-1 .1282 .9042-1 20'60' .7778 -1 .874-5-1 .1255 .9033 -1 10'

31"00' .7795-1 I .877l -1 '. .1229 .9023 -1 53° 00'10' .7811 -1 .8797-1 .1203 .9014 -1 50'20' .7828 -1 .8824-1 . .1176 .9004 -1 40'30' .7844 -1 .8850-1 .1150 .8995 -1 30'40' .7861 1 .8876-1 .1124 .8985-1 20'50' .7877 -1 .8902-1 .1098 .8975 -1 10'

3'. 00' .7893 -1 '.8928-1 '.1072 .8965-1 52° 00',10' .7910...,.1 .89M -1 .1046 .8955-1 50'20' .7926 -1 .898(}-1 .1020 .8945-1 40'30' .7941-1 .9006-1 .0994 .8935-1 30'40' .7957 -1 .9032-1 .0968 . .8Q25-1 20'60' .7973 -1 .9058-1 ' .0942 .8915-1 10'

3 00' .7989 -1 .9084-1 .0916 .8905 -' 1 51° 00',lO' .8004 -1 .9110-1 .0890 .8895-1 50'-20' . .8020-1 .9186-1 .0865 .8884 -:-1 40'30' .8035 -1 .9161-1 .0839 .8874 -1 30'40' .8050 -1 .9187-1 .0813 .8864 - 1 20'50' .8066 - 1 .9212-1 .0788 .8853- 1 10'

"0° 00' .8081 -1 .9238-1 .0762 .8843 - 1 50° 00' t'10' .8096 -1 , .92M-1 .0736 .8832-1 50'20' .8111 -1 .9289'-:'1 .0711 \ .,8821 -1 40'aO' .8125 -1 .9315-1 .0685 .8810-1 '30'40' .8140-1 .9341-1 .0659 .8800-1 20'50' .8155-1 .9366-1 .0634 .8789-1 10'-

41° 00' .8169-1 . .9392-1 .0608 .8778-1 ..po00'10' .8184-1 .941'7-f .0583 .8767 -1 50'20' .8198-1 .9443-1 .0557 .8756-=1 40'30' .8213-1 .9468-1 .0532 .8745-1 30'40' :8217-1 .9494-1 .0506 .8733-1 20'50' .8241-1 .9519-1 .0481 .8722- 1 10'

'2. I

.8255--1 .9M4 -1 .0456 .8711-1 ..ao 00'

.8269....1 .9510-1 .0430 .8699- 1 50'I 20' .8283 -1 .9596 -1 .0405 .8088 -1 40'I ,;;0' .f\2';}7- 1 .9621 -1 .0379 .8676-1 . 30'I ';'0' '.8;:'. 1- 1 , .9846-1 .03M .8665 :...:.1 20', ".ty .8324- 1

I

.9671-1 .0329-

.8653 -1 10'Io ..:"'-' I .83.38- 1 .96f.: ....J .0303 .8641-1 "7° 00'

", I ')351-1 .9722 --¡ .0278 .8629 -1 50'W' I .¡.,3, -1 J

.9147-] .0253 .8618 -1 40'vf.l .8378 -1 .iJ772- A 0228 .8606 - 1 30'

I40' I .Sj91 --1 .9798-1 .0202 .8594- 1 20'

I 50'. I .8405-1 .982:1-l. .0177 .8582- 1 10'; ....1100' I .8418-1 .9848-1 .0162 .8569-1 "6° 00'I 10' I .843i -1 . .987:4-l. .0126 .8567-1 50'I 20' I .84« - 1 .9899-1 .0101 .8545- 1 40'

30' I

.1H67-.1 .9924.,..1 .0076 .8532- 1 30'40' .8469-1 .9949-1 .0051 .8520-1 20'".

I.84S2-1 .9975 .-1 .0025 .8501- 1 10'

, 0'11 ..8495-1 - '- n:" --- .0000 .8495-1 45° 00'I'-'

Log Sos I l'vg(.r Log T ! Log Sen Grados Il_.-