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Exercises 20.6, page 563

1. y is the angle whose tangent is 3A.
3. 0
5. y is the angle whose tangent is 5x.
7. y is twice the angle whose sine is x.
9. y is five times the angle whose cosine is $2 x - 1 .$ $2 x - 1 .$
11. $\frac{π}{3}$ $\frac{π}{3}$
13. $\frac{π}{4}$ $\frac{π}{4}$
15. $- \frac{π}{3}$ $- \frac{π}{3}$
17. No value
19. $- \frac{π}{4}$ $- \frac{π}{4}$
21. $\frac{1}{2} \sqrt{3}$ $\frac{1}{2} \sqrt{3}$
23. $\frac{π}{4}$ $\frac{π}{4}$
25. $\frac{\sqrt{26}}{26}$ $\frac{\sqrt{26}}{26}$
27. $- 1$ $- 1$
29. $- 1.2303$ $- 1.2303$
31. 0.0219
33. $- 1.2389$ $- 1.2389$
35. $- 0.2239$ $- 0.2239$
37. $x = \frac{1}{3} \sin^{- 1} y$ $x = \frac{1}{3} \sin^{- 1} y$
39. $x = 4 \tan y$ $x = 4 \tan y$
41. $x = 1 - \cos (1 - y)$ $x = 1 - \cos (1 - y)$
43. $\frac{x}{\sqrt{1 - x^{2}}}$ $\frac{x}{\sqrt{1 - x^{2}}}$
45. $\frac{\sqrt{x^{2} - 16}}{x}$ $\frac{\sqrt{x^{2} - 16}}{x}$
47. $\frac{3 x}{\sqrt{9 x^{2} - 1}}$ $\frac{3 x}{\sqrt{9 x^{2} - 1}}$
49. $2 x \sqrt{1 - x^{2}}$ $2 x \sqrt{1 - x^{2}}$
51. No: $\sin^{- 1} (\sin x) = x for - \frac{π}{2} \leq x \leq \frac{π}{2} .$ $\sin^{- 1} (\sin x) = x for - \frac{π}{2} \leq x \leq \frac{π}{2} .$
53. $A = area of sector - area of triangle$ $A = area of sector - area of triangle$
55. $t = \frac{1}{ω} (\sin^{- 1} \frac{i}{I_{m}} - α - ϕ)$ $t = \frac{1}{ω} (\sin^{- 1} \frac{i}{I_{m}} - α - ϕ)$
57. $\sin (\sin^{- 1} \frac{3}{5} + \sin^{- 1} \frac{5}{13}) = \frac{3}{5} \cdot \frac{12}{13} + \frac{4}{5} \cdot \frac{5}{13} = \frac{56}{65}$ $\sin (\sin^{- 1} \frac{3}{5} + \sin^{- 1} \frac{5}{13}) = \frac{3}{5} \cdot \frac{12}{13} + \frac{4}{5} \cdot \frac{5}{13} = \frac{56}{65}$
59. $- \frac{\sqrt{2}}{10}$ $- \frac{\sqrt{2}}{10}$
61. $x y + \sqrt{1 - x^{2} - y^{2} + x^{2} y^{2}}$ $x y + \sqrt{1 - x^{2} - y^{2} + x^{2} y^{2}}$
63. $\frac{π}{2}$ $\frac{π}{2}$
65. 0
67. $\sin^{- 1} (\frac{a}{c})$ $\sin^{- 1} (\frac{a}{c})$
69. $\tan^{- 1} (\frac{b \tan B}{a})$ $\tan^{- 1} (\frac{b \tan B}{a})$
71. Let $y = height$ $y = height$ to top of pedestal;
$\tan α = \frac{151 + y}{d}, \tan β = \frac{y}{d}; \tan α = \frac{151 + d \tan β}{d}$ $\tan α = \frac{151 + y}{d}, \tan β = \frac{y}{d}; \tan α = \frac{151 + d \tan β}{d}$
73. $θ = \tan^{- 1} (\frac{y + 50}{x}) - \tan^{- 1} (\frac{y}{x})$ $θ = \tan^{- 1} (\frac{y + 50}{x}) - \tan^{- 1} (\frac{y}{x})$
75. $θ = π - \tan^{- 1} (\frac{50}{x}) - \tan^{- 1} (\frac{25}{35 - x})$ $θ = π - \tan^{- 1} (\frac{50}{x}) - \tan^{- 1} (\frac{25}{35 - x})$

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Table of Contents for Exercises 20.6, page 563

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Table of Contents for
Exercises 20.6, page 563