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Exercises 20.3, page 549

1. $- \sqrt{3}$ $- \sqrt{3}$
3. $- \frac{24}{25}$ $- \frac{24}{25}$
5.

$\begin{array}{l} \sin 60 ° = \sin 2 (30 °) = 2 \sin 30 ° \cos 30 ° \\ = 2 (\frac{1}{2}) (\frac{1}{2} \sqrt{3}) = \frac{1}{2} \sqrt{3} \end{array}$ $\begin{array}{l} \sin 60 ° = \sin 2 (30 °) = 2 \sin 30 ° \cos 30 ° \\ = 2 (\frac{1}{2}) (\frac{1}{2} \sqrt{3}) = \frac{1}{2} \sqrt{3} \end{array}$
7. $\tan 120 ° = \frac{2 \tan 60 °}{1 - \tan^{2} 60 °} = \frac{2 \sqrt{3}}{1 - {(\sqrt{3})}^{2}} = - \sqrt{3}$ $\tan 120 ° = \frac{2 \tan 60 °}{1 - \tan^{2} 60 °} = \frac{2 \sqrt{3}}{1 - {(\sqrt{3})}^{2}} = - \sqrt{3}$
9. $\sin 100 ° = 2 \sin 50 ° \cos 50 ° = 0.9848$ $\sin 100 ° = 2 \sin 50 ° \cos 50 ° = 0.9848$
11. $\cos 96 ° = \cos^{2} 48 ° - \sin^{2} 48 ° = - 0.1045285$ $\cos 96 ° = \cos^{2} 48 ° - \sin^{2} 48 ° = - 0.1045285$
13.

$\begin{array}{l} \tan \frac{2 π}{7} & = \frac{2 \tan \frac{π}{7}}{1 - \tan^{2} \frac{π}{7}} \\ = 1.254 \end{array}$ $\begin{array}{l} \tan \frac{2 π}{7} & = \frac{2 \tan \frac{π}{7}}{1 - \tan^{2} \frac{π}{7}} \\ = 1.254 \end{array}$
15. $\frac{24}{25}$ $\frac{24}{25}$
17. $- \sqrt{3}$ $- \sqrt{3}$
19. $3 \sin 10 x$ $3 \sin 10 x$
21. $\cos 8 x$ $\cos 8 x$
23. $\cos x$ $\cos x$
25. $- 4 \cos 4 x$ $- 4 \cos 4 x$
27. $2 \sin 3 θ$ $2 \sin 3 θ$
29. 2
31. $\cos^{2} α - (1 - \cos^{2} α)$ $\cos^{2} α - (1 - \cos^{2} α)$
33. $\frac{\cos x - (\sin x / \cos x) \sin x}{1 / \cos x} = \cos^{2} x - \sin^{2} x$ $\frac{\cos x - (\sin x / \cos x) \sin x}{1 / \cos x} = \cos^{2} x - \sin^{2} x$
35. $\frac{2 \sin θ \cos θ}{1 + 2 \cos^{2} θ - 1} = \frac{\sin θ}{\cos θ}$ $\frac{2 \sin θ \cos θ}{1 + 2 \cos^{2} θ - 1} = \frac{\sin θ}{\cos θ}$
37. $1 - (1 - 2 \sin^{2} 2 θ) = \frac{2}{\csc^{2} θ}$ $1 - (1 - 2 \sin^{2} 2 θ) = \frac{2}{\csc^{2} θ}$
39. $\ln \frac{1 - \cos 2 x}{1 + \cos 2 x} = \ln \frac{2 \sin^{2} x}{2 \cos^{2} x} = {\ln tan}^{2} x$ $\ln \frac{1 - \cos 2 x}{1 + \cos 2 x} = \ln \frac{2 \sin^{2} x}{2 \cos^{2} x} = {\ln tan}^{2} x$
41.
43.
45. $3 \sin x - 4 \sin^{3} x$ $3 \sin x - 4 \sin^{3} x$
47. $8 \cos^{4} x - 8 \cos^{2} x + 1$ $8 \cos^{4} x - 8 \cos^{2} x + 1$
49. 1
51. $\log \cos 2 x$ $\log \cos 2 x$
53. $amp . = 2, per . = π;$ $amp . = 2, per . = π;$ write equation as $y = 2 (2 \sin x \cos x) = 2 \sin 2 x .$ $y = 2 (2 \sin x \cos x) = 2 \sin 2 x .$
55. $\sqrt{\sin^{2} x + 2 \sin x \cos x + \cos^{2} x} = \sqrt{1 + \sin 2 x}$ $\sqrt{\sin^{2} x + 2 \sin x \cos x + \cos^{2} x} = \sqrt{1 + \sin 2 x}$
57. 474 m
59. $R = v (\frac{2 v \sin α}{g}) \cos α = \frac{v^{2} (2 \sin α \cos α)}{g}$ $R = v (\frac{2 v \sin α}{g}) \cos α = \frac{v^{2} (2 \sin α \cos α)}{g}$
61.

$\begin{array}{l} v i \sin ω t \sin (ω t - \frac{π}{2}) \\ = v i \sin ω t (\sin ω t \cos \frac{π}{2} - \cos ω t \sin \frac{π}{2}) \\ = v i \sin ω t [- (\cos ω t) (1)] = - \frac{1}{2} vi (2 \sin ω t \cos ω t) \end{array}$ $\begin{array}{l} v i \sin ω t \sin (ω t - \frac{π}{2}) \\ = v i \sin ω t (\sin ω t \cos \frac{π}{2} - \cos ω t \sin \frac{π}{2}) \\ = v i \sin ω t [- (\cos ω t) (1)] = - \frac{1}{2} vi (2 \sin ω t \cos ω t) \end{array}$

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Table of Contents for Exercises 20.3, page 549

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Table of Contents for
Exercises 20.3, page 549