Example M-9 Cosine of a Sum
Using the suitable trigonometric identity from Table M-2, find cos(135° + 22°). Give your answer with four significant figures.
Set Up
As long as all angles are given in degrees, there is no need to convert to radians, because all operations are numerical ­values
of the functions. Be sure, however, that your calculator is in degree mode. The suitable identity is cos(A { B) = cos A cos
B | sin A sin B, where the upper signs are appropriate.
Solve
Write the trigonometric identity for the cosine of a sum,
with A = 135° and B = 22°:
Using a calculator, find cos 135°, sin 135°, cos 22°,
and sin 22°:
Enter the values in the formula and calculate the answer:
cos 1135 + 222 = 1cos 1352 1cos 222
- 1sin 1352 1sin 222
cos 135
cos 22
sin 135
sin 22
=
=
=
=
- 0.7071
0.9272
0.7071
0.3746
cos 1135 + 222 = 1 - 0.70712 10.92722
- 10.70712 10.37462
= - 0.9205
Reflect
The calculator shows that cos(135° + 22°) = cos(157°) = 20.9205.
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