PHILOSOPHY |
PHILOSOPHY |
…
Mathematics: Trigonometric Tables
PI = 3.141592… (approximately 3.1428) radians = degress x PI / 180 (deg to rad conversion) degress = radians x 180 / PI (rad to deg conversion) |
Rad | Deg | Sin | Cos | Tan | Csc | Sec | Cot | ||
---|---|---|---|---|---|---|---|---|---|
.0000 | 00 | .0000 | 1.0000 | .0000 | —– | 1.0000 | —– | 90 | 1.5707 |
.0175 | 01 | .0175 | .9998 | .0175 | 57.2987 | 1.0002 | 57.2900 | 89 | 1.5533 |
.0349 | 02 | .0349 | .9994 | .0349 | 28.6537 | 1.0006 | 28.6363 | 88 | 1.5359 |
.0524 | 03 | .0523 | .9986 | .0524 | 19.1073 | 1.0014 | 19.0811 | 87 | 1.5184 |
.0698 | 04 | .0698 | .9976 | .0699 | 14.3356 | 1.0024 | 14.3007 | 86 | 1.5010 |
.0873 | 05 | .0872 | .9962 | .0875 | 11.4737 | 1.0038 | 11.4301 | 85 | 1.4835 |
.1047 | 06 | .1045 | .9945 | .1051 | 9.5668 | 1.0055 | 9.5144 | 84 | 1.4661 |
.1222 | 07 | .1219 | .9925 | .1228 | 8.2055 | 1.0075 | 8.1443 | 83 | 1.4486 |
.1396 | 08 | .1392 | .9903 | .1405 | 7.1853 | 1.0098 | 7.1154 | 82 | 1.4312 |
.1571 | 09 | .1564 | .9877 | .1584 | 6.3925 | 1.0125 | 6.3138 | 81 | 1.4137 |
.1745 | 10 | .1736 | .9848 | .1763 | 5.7588 | 1.0154 | 5.6713 | 80 | 1.3953 |
.1920 | 11 | .1908 | .9816 | .1944 | 5.2408 | 1.0187 | 5.1446 | 79 | 1.3788 |
.2094 | 12 | .2079 | .9781 | .2126 | 4.8097 | 1.0223 | 4.7046 | 78 | 1.3614 |
.2269 | 13 | .2250 | .9744 | .2309 | 4.4454 | 1.0263 | 4.3315 | 77 | 1.3439 |
.2443 | 14 | .2419 | .9703 | .2493 | 4.1336 | 1.0306 | 4.0108 | 76 | 1.3265 |
.2618 | 15 | .2588 | .9659 | .2679 | 3.8637 | 1.0353 | 3.7321 | 75 | 1.3090 |
.2793 | 16 | .2756 | .9613 | .2867 | 3.6280 | 1.0403 | 3.4874 | 74 | 1.2915 |
.2967 | 17 | .2924 | .9563 | .3057 | 3.4203 | 1.0457 | 3.2709 | 73 | 1.2741 |
.3142 | 18 | .3090 | .9511 | .3249 | 3.2361 | 1.0515 | 3.0777 | 72 | 1.2566 |
.3316 | 19 | .3256 | .9455 | .3443 | 3.0716 | 1.0576 | 2.9042 | 71 | 1.2392 |
.3491 | 20 | .3420 | .9397 | .3640 | 2.9238 | 1.0642 | 2.7475 | 70 | 1.2217 |
.3665 | 21 | .3584 | .9336 | .3839 | 2.7904 | 1.0711 | 2.6051 | 69 | 1.2043 |
.3840 | 22 | .3746 | .9272 | .4040 | 2.6695 | 1.0785 | 2.4751 | 68 | 1.1868 |
.4014 | 23 | .3907 | .9205 | .4245 | 2.5593 | 1.0864 | 2.3559 | 67 | 1.1694 |
.4189 | 24 | .4067 | .9135 | .4452 | 2.4586 | 1.0946 | 2.2460 | 66 | 1.1519 |
.4363 | 25 | .4226 | .9063 | .4663 | 2.3662 | 1.1034 | 2.1445 | 65 | 1.1345 |
.4538 | 26 | .4384 | .8988 | .4877 | 2.2812 | 1.1126 | 2.0503 | 64 | 1.1170 |
.4712 | 27 | .4540 | .8910 | .5095 | 2.2027 | 1.1223 | 1.9626 | 63 | 1.0996 |
.4887 | 28 | .4695 | .8829 | .5317 | 2.1301 | 1.1326 | 1.8807 | 62 | 1.0821 |
.5061 | 29 | .4848 | .8746 | .5543 | 2.0627 | 1.1434 | 1.8040 | 61 | 1.0647 |
.5236 | 30 | .5000 | .8660 | .5774 | 2.0000 | 1.1547 | 1.7321 | 60 | 1.0472 |
.5411 | 31 | .5150 | .8572 | .6009 | 1.9416 | 1.1666 | 1.6643 | 59 | 1.0297 |
.5585 | 32 | .5299 | .8480 | .6249 | 1.8871 | 1.1792 | 1.6003 | 58 | 1.0123 |
.5760 | 33 | .5446 | .8387 | .6494 | 1.8361 | 1.1924 | 1.5399 | 57 | .9948 |
.5934 | 34 | .5592 | .8290 | .6745 | 1.7883 | 1.2062 | 1.4826 | 56 | .9774 |
.6109 | 35 | .5736 | .8192 | .7002 | 1.7434 | 1.2208 | 1.4281 | 55 | .9599 |
.6283 | 36 | .5878 | .8090 | .7265 | 1.7013 | 1.2361 | 1.3764 | 54 | .9425 |
.6458 | 37 | .6018 | .7986 | .7536 | 1.6616 | 1.2521 | 1.3270 | 53 | .9250 |
.6632 | 38 | .6157 | .7880 | .7813 | 1.6243 | 1.2690 | 1.2799 | 52 | .9076 |
.6807 | 39 | .6293 | .7771 | .8098 | 1.5890 | 1.2868 | 1.2349 | 51 | .8901 |
.6981 | 40 | .6428 | .7660 | .8391 | 1.5557 | 1.3054 | 1.1918 | 50 | .8727 |
.7156 | 41 | .6561 | .7547 | .8693 | 1.5243 | 1.3250 | 1.1504 | 49 | .8552 |
.7330 | 42 | .6691 | .7431 | .9004 | 1.4945 | 1.3456 | 1.1106 | 48 | .8378 |
.7505 | 43 | .6820 | .7314 | .9325 | 1.4663 | 1.3673 | 1.0724 | 47 | .8203 |
.7679 | 44 | .6947 | .7193 | .9657 | 1.4396 | 1.3902 | 1.0355 | 46 | .8029 |
.7854 | 45 | .7071 | .7071 | 1.0000 | 1.4142 | 1.4142 | 1.0000 | 45 | .7854 |
Cos | Sin | Cot | Sec | Csc | Tan | Deg | Rad |
Continue reading |
Since Conversion from “Autocad 2009 to Autocad 2010” … may not always open, work and/ or load correctly. use AutoCAD 2010
SOHCAHTOA is a handy way to memorize the follow formulas. especially when you need to know how to compute the sine, cosine, and tangent of an angle.
SOH stands for Sine equals Opposite over Hypotenuse.
CAH stands for Cosine equals Adjacent over Hypotenuse.
TOA stands for Tangent equals Opposite over Adjacent.
Inverse Cosinecos-1Cos-1arccosArccos
The inverse function of cosine.
Basic idea: To find cos-1 (½), we ask “what angle has cosine equal to ½?” The answer is 60°. As a result we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.
More: There are actually many angles that have cosine equal to ½. We are really asking “what is the simplest, most basic angle that has cosine equal to ½?” As before, the answer is 60°. Thus cos-1 (½) = 60° or cos-1 (½) = π/3.
Details: What is cos-1 (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.
In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].
Note: arccos refers to “arc cosine”, or the radian measure of the arc on a circle corresponding to a given value of cosine.
Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or Cos-1). However, most mathematicians do not follow this practice. This website does not distinguish between capitalized and uncapitalized trig functions.
From: http://www.mathwords.com/c/cosine_inverse.htm
Already a Member? Login