Practice and Applications

7.

$\begin{array}{l} \sin (90 ° + 30 °) = \sin 90 ° \cos 30 ° + \cos 90 ° \sin 30 ° \\ = (1) (\frac{1}{2} \sqrt{3}) + (0) (\frac{1}{2}) = \frac{1}{2} \sqrt{3} \end{array}$
9.

$\begin{array}{l} \sin (360 ° - 45 °) = \sin 360 ° \cos 45 ° - \cos 360 ° \sin 45 ° \\ = 0 (\frac{1}{2} \sqrt{2}) - 1 (\frac{1}{2} \sqrt{2}) = - \frac{1}{2} \sqrt{2} \end{array}$
11. $\cos (2 \frac{π}{2}) = \cos^{2} \frac{π}{2} - \sin^{2} \frac{π}{2} = 0 - 1^{2} = - 1$
13. $\tan 2 (30 °) = \frac{2 \tan 30 °}{1 - \tan^{2} 30 °} = \frac{2 (\sqrt{3} / 3)}{1 - {(\sqrt{3} / 3)}^{2}} = \sqrt{3}$
15. $\sin 50 ° = 0.76604$
17. $\sin (\frac{π}{7}) = 0.43388$
19. $\cos 215 ° = - 0.8192$
21. $\tan 36 ° = 0.72654$
23. $\sin 5 x$
25. $2 \sin 14 x$
27. $2 \cos 12 x$
29. $2 \cos x$
31. $- \frac{π}{2}$
33. 0.5298
35. $- \frac{1}{3} \sqrt{3}$
37. $- \frac{π}{3}$
39. $\sec^{2} y - \tan^{2} y = 1$
41. $\sin x \csc x - \sin^{2} x = 1 - \sin^{2} x = \cos^{2} x$
43. $\frac{(\sec^{2} x - 1) (\sec^{2} x + 1)}{\tan^{2} x} = \sec^{2} x + 1$
45. $\begin{array}{l} 2 (\frac{1}{\sin 2 x}) (\frac{\cos x}{\sin x}) = 2 (\frac{1}{2 \sin x \cos x}) (\frac{\cos x}{\sin x}) \\ = \frac{1}{\sin^{2} x} = \csc^{2} x \end{array}$
47. $\frac{\cos^{2} θ}{\sin^{2} θ}$
49. $\frac{1}{2} (2 sin ...$

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