James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A32
appendix D Trigonometry
Exercises
1–6 Convert from degrees to radians.
1. 2108 2. 3008 3. 98
4. 23158 5. 9008 6. 368
7–12 Convert from radians to degrees.
7. 4 8. 2 7 2
10.
8
3
11. 2 3 8
9.
12. 5
5
12
13. Find the length of a circular arc subtended by an angle of
y12 rad if the radius of the circle is 36 cm.
14. If a circle has radius 10 cm, find the length of the arc subtended
by a central angle of 728.
15. A circle has radius 1.5 m. What angle is subtended at the
center of the circle by an arc 1 m long?
16. Find the radius of a circular sector with angle 3y4 and arc
length 6 cm.
17–22 Draw, in standard position, the angle whose measure is
given.
17. 3158 18. 21508 19. 2 3 4 rad
7
20. rad 21. 2 rad 22. 23 rad
3
23–28 Find the exact trigonometric ratios for the angle whose
radian measure is given.
3
4
23.
24.
4
3
5
26. 25 27.
6
29–34 Find the remaining trigonometric ratios.
29. sin − 3 5 , 0 , , 2
30. tan − 2, 0 , , 2
31. sec − 21.5, 2 , ,
32. cos x − 2 1 3 , , x , 3 2
33. cot − 3, , , 2
34. csc − 2 4 3 , 3 2 , , 2
9
25.
2
11
28.
4
35–38 Find, correct to five decimal places, the length of the side
labeled x.
x
35.
36. 40° x
40°
10 cm
x
10 cm
25 cm
x
25 cm
35°
35°
37.
2π
5
x
2π
5
8 cm
8 cm
39–41 Prove each equation.
x
38.
22 cm
22 cm
39. (a) Equation 10a (b) Equation 10b
40. (a) Equation 14a (b) Equation 14b
41. (a) Equation 18a
(c) Equation 18c
42–58 Prove the identity.
42. cosS 2 2 x D − sin x
3π
8
x
3π
8
(b) Equation 18b
43. sinS 2 1 x D − cos x 44. sins 2 xd − sin x
45. sin cot − cos 46. ssin x 1 cos xd 2 − 1 1 sin 2x
47. sec y 2 cos y − tan y sin y
48. tan 2 2 sin 2 − tan 2 sin 2
49. cot 2 1 sec 2 − tan 2 1 csc 2
50. 2 csc 2t − sec t csc t
51. tan 2 −
52.
2 tan
1 2 tan 2
1
1 2 sin 1 1
1 1 sin − 2 sec2
53. sin x sin 2x 1 cos x cos 2x − cos x
54. sin 2 x 2 sin 2 y − sinsx 1 yd sinsx 2 yd
55.
sin
− csc 1 cot
1 2 cos
56. tan x 1 tan y −
sinsx 1 yd
cos x cos y
x
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