How to Use a Trigonometric
Functions Table
The trigonometry functions table provides a convenient way to look-up the values for degrees of an angle and its sine, cosine, tangent and cotangent of that angle. The angle values listed in the table range from 0° to 90° with each angle degree sub-divided by 10 minute intervals.
To find a value for an angle of 0° to 45°; first find the trig function in question from the top column headings. Then, read down and locate the angle in the column labeled degrees.
To find a value for an angle of 45° to 90°; first find the trig function in question from the bottom column headings. Then, read up and locate the angle in the column labeled degrees.
Trig functions table entries for 27°00’ thru 29°50’ and 60°10’ thru 63°:
Degrees | Radians | Sine | Tangent | Cotangent | Cosine | ||
27°00’ | .4712 | .0000 | .5095 | 1.9626 | .8910 | 1.0996 | 63°00’ |
10’ | .4741 | .4566 | .5132 | 1.9486 | .8897 | 1.0966 | 50’ |
20’ | .4771 | .4592 | .5169 | 1.9347 | .8884 | 1.0937 | 40’ |
30’ | .4800 | .4617 | .5206 | 1.9210 | .8870 | 1.0908 | 30’ |
40’ | .4829 | .4643 | .5243 | 1.9074 | .8857 | 1.0879 | 20’ |
50’ | .4858 | .4669 | .5280 | 1.8940 | .8843 | 1.0850 | 10’ |
28°00’ | .4887 | .4695 | .5317 | 1.8807 | .8829 | 1.0821 | 62°00’ |
10’ | .4916 | .4720 | .5354 | 1.8676 | .8816 | 1.0792 | 50’ |
20’ | .4945 | .4746 | .5392 | 1.8546 | .8802 | 1.0763 | 40’ |
30’ | .4974 | .4772 | .5430 | 1.8418 | .8788 | 1.0734 | 30’ |
40’ | .5003 | .4797 | .5467 | 1.8291 | .8774 | 1.0705 | 20’ |
50’ | .5032 | .4823 | .5505 | 1.8165 | .8760 | 1.0676 | 10’ |
29°00’ | .5061 | .4848 | .5543 | 1.8040 | .8746 | 1.0647 | 61°00’ |
10’ | .5091 | .4874 | .5581 | 1.7917 | .8732 | 1.0617 | 50’ |
20’ | .5120 | .4899 | .5619 | 1.7796 | .8718 | 1.0588 | 40’ |
30’ | .5149 | .4924 | .5658 | 1.7675 | .8704 | 1.0559 | 30’ |
40’ | .5178 | .4950 | .5696 | 1.7556 | .8689 | 1.0530 | 20’ |
50’ | .5207 | .4975 | .5735 | 1.7437 | .8675 | 1.0501 | 10’ |
Cosine | Cotangent | Tangent | Sine | Radians | Degrees |
Above we can see that .5581 is the tangent of 29°10’. We can also see that the cotangent of 60°50’, the compliment of the tangent, is .5581.
The trig table is structured this way because a right angle triangle by definition has one angle that is 90°; the remaining 2 angles must sum to 90° (so that the total of the 3 angles is 180°). Listing the functions for a given angle with its compliment angle just makes sense.
Should a greater accuracy be required, beyond 10 minute intervals, interpolation can be applied. Any error introduced by interpolation is negligible and is due to the rounding of the fourth decimal digit of table entries. As an example of interpolation, to determine the sine of 29°15’; subtract the sine of 29°10’ from the sine of 29°20’, divide this result by 2 and add this result to 29°10’:
(.4899 − .4874) / 2 = .00125
.4874 + .00125 = .48865 = .4887 = sine 29°15’
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