Exercises 20.2, page 546

1. $\frac{16}{65}$
3.

$\begin{array}{l} \sin 105 ° = \sin 60 ° \cos 45 ° + \cos 60 ° \sin 45 ° \\ = \frac{\sqrt{3}}{2} \frac{\sqrt{2}}{2} + \frac{1}{2} \frac{\sqrt{2}}{2} = 0.9659 \end{array}$
5.

$\begin{array}{l} \cos 15 ° = \cos (60 ° - 45 °) = \cos 60 ° \cos 45 ° + \sin 60 ° \sin 45 ° \\ = (\frac{1}{2}) (\frac{1}{2} \sqrt{2}) + (\frac{1}{2} \sqrt{3}) (\frac{1}{2} \sqrt{2}) \\ = \frac{1}{4} \sqrt{2} + \frac{1}{4} \sqrt{6} = \frac{1}{4} (\sqrt{2} + \sqrt{6}) = 0.9659 \end{array}$
7. $- \frac{33}{65}$
9. $- \frac{56}{65}$
11. $\sin 3 x$
13. $\cos 4 x$
15. $\cos x$
17. $\tan x$
19. 0
21. 1
23. 0
25.

$\begin{array}{l} (\sin x \cos y + \cos x \sin y) (\sin x \cos y - \cos x \sin y) \\ = \sin^{2} x \cos^{2} y - \cos^{2} x \sin^{2} y \\ = \sin^{2} x (1 - \sin^{2} y) - (1 - \sin^{2} x) \sin^{2} y = \sin^{2} x - \sin^{2} y \end{array}$

Get Basic Technical Mathematics, 11th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans