Chapter 10

1 – 29. Check your answers on a calculator.

32. Sine and cosine have range $ [-1,1] $ . Tangent’s range is all real numbers.

33. Check your answers on a calculator. 34. -5, $ 10^{10} $ , $ /e $

34. For all $ $ , the slope of OP is $ = = = $ .

35. $ f(x) = x + 1 $ is neither even nor odd, since $ f(-1) = 0 $ , but $ f(1) = 2 $ .

\[ \mathbf{9.}\;1+\tan^{2}\theta=\sec^{2}\theta\quad\mathbf{40.}\;1+\cot^{2}\theta=\csc^{2}\theta\quad\mathbf{41.}\;\cos\left(180^\circ-\theta\right)=-\cos\theta\quad\mathbf{42.}\;\sin\left(180^\circ-\theta\right)=\sin\theta \]

43. 1. $ (+ 90^{}) = $ b) $ (+ 90^{}) = -$ c) $ (+ 90^{}) = -$

4. $ (- 90^{}) = -$ e) $ (- 90^{}) = $ f) $ (- 90^{}) = -$

5. cos(θ + 180°) = − cos θ h) cos(θ − 180°) = − cos θ i) sin(θ + 180°) = − sin θ

6. $ (- 180^{}) = -$ k) $ (180^{} + ) = $ l) $ (- 180^{}) = $

44. 1. $ $ b) $ -$ c) $ ^{2}$ d) -1 e) $ -x $ f) 1

45. The claim is true. [Proof: If f is odd, then $ f(0) = -f(-0) $ , but -0 = 0, so this last equation tells us that $ f(0) = -f(0) $ . That is, $ f(0) $ equals its own negative. Since the only such number is 0, we conclude that $ f(0) = 0 $ . Hence the graph passes through the origin.]

46. $ f(x) = 0. $

Chapter 11

1. 1. The remaining parts are $ 46^{} $ , 6.56, 4.93, b) $ 51^{} $ , 0.97, 1.27, c) $ 66^{} $ , 0.81, 1.83
2. 1. $ 37^{} $ , 4.54, 5.16 b) $ 28^{} $ , 18.81, 21.30 c) $ 41^{} $ , 5.57, 7.62 6. 106.65 cubits
3. 1. 70.1°, 44.9°, 3.85 b) 45.2°, 83.5°, 51.3° c) 67.4°, 22.6°, 12 d) 54°, 123.57, 150.86

4. $ x $ 11. a) 639 feet b) 75 feet c) 12:27 am

5. 2. no c) yes, $ 48.6^{} $ d) yes, $ 131.4^{} $ (the supplement of $ 48.6^{} $ ) e) yes, $ 41.4^{} $ 17. $ /4 $ units $ ^{2} $
6. 1. $ /2 $ units $ ^{2} $ b) 30 units $ ^{2} $ c) $ 2 $ units $ ^{2} $ 19. a) 12.62 units $ ^{2} $ b) 0.18 units $ ^{2} $

Chapter 12

1. 2. 90°, c) 60°, n) 210°, o) 330°, p) 27°
2. 1. π/6, b) π/4, c) π/3, n) 3π/4, o) 5π/4, p) 7π/4
3. 1. $ (180/)^{} ^{} $ b) $ (540/)^{} ^{} $ c) $ 1^{} $
4. 1. $ /12 $ , b) $ /18 $ , c) $ /180 $ , d) $ 8/45 $ , e) $ 53/45 $ , g) approximately .094 radians.

5. Check your answers with a calculator. 6. a) arc length = $ (/180)r$ b) arc length = $ r$ .

6. 1. sector area = (π/360)r²θ b) sector area = (1/2)r²θ. 8. Approximately 0.523 units².

7. Approximately 1.967 units $ ^{2} $ and 32.590 units $ ^{2} $ . 12. $ p() = $ 13. a, c, e, g are FALSE.

8. $ (+ 2k) = $ for all integers k. 16. Check on a computer.

9. 1. Hint: Drop a perpendicular from P to the x-axis, then use similar triangles. c) section, dissect, tangible.

4. $ 1 + ^{2} = ^{2} $ , which you can see by applying the Pythagorean Theorem to $ OTQ $ .

19. Many possibilities exist for each, the simplest being…

\[ \mathsf{a})y=4\sin\left(\frac{\pi}{5}x\right)+3,\quad\mathsf{b})y=22\cos\left(\frac{\pi}{7}x\right)-6,\quad\mathsf{c})y=-\frac{1}{2}\sin\left(\frac{2\pi}{3}x\right)-2,\quad\mathsf{d})y=\pi\sin(\pi x)-\pi \]

23. 1. No. The function is undefined at 0. b) Infinitely many times. c) The greatest solution: $ 1/$ .
24. Check your graphs on a computer.