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The trigonometry functions table provides a convenient way to lookup 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 subdivided 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 20°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’