1. Unit 7 Trigonometric Graphs Review Problems
PreCalculus 4-R

2. Unit 4 Test The test is in two parts Part 1 Part 2
Calculator allowed (necessary) – 50%
Part 2
Graphing calculator not allowed – 50%
Unit 4 Test

3. 1
Review Problems

4. 2
Review Problems

5. 3
Review Problems

6. 4
Review Problems

7. 5
Review Problems

8. 6
Review Problems

9. 7
Review Problems

10. 8
Review Problems

11. 9
Review Problems

12. 10
Review Problems

13. 11
Review Problems

14. 12
Review Problems

15. 13
Review Problems

16. 14
Review Problems

17. 15
Review Problems

18. 16
Review Problems

19. 17
Review Problems

20. 18
Review Problems

21. 19
Review Problems

22. 20
Review Problems

23. 21
Review Problems

24. 22
Review Problems

25. 23
Review Problems

26. 24
Review Problems

27. 25
Review Problems

28. 26
Review Problems

29. 27
Review Problems

30. 28
Review Problems

31. 29
Review Problems

32. 30
Review Problems

33. 31
Review Problems

34. 32
Review Problems

35. 33
Review Problems

36. 34
Review Problems

37. 35
Review Problems

38. 36
Review Problems

39. Find all exact values of t for which the given statement is true37
Review Problems

40. Find all exact values of t for which the given statement is true38
Review Problems

41. Find all exact values of t for which the given statement is true39
Review Problems

42. Find all exact values of t for which the given statement is true40
Review Problems

43. 41
Review Problems

44. 42
Review Problems

45. 43
Review Problems

46. -1 1 44
Review Problems

47. 45 Review Problems Find the degree measure of the angle: 12°
-450° 45
Review Problems

48. To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has radius 3.2 m and rotates at 100 rpm, find the speed of the current in m/s.
33.51 46
Review Problems

49. 47 Review Problems Find sin a and cos B if x = 4, and y = 1.
sin a = , cos = 47
Review Problems

50. What is the side labeled x equal to, if y = 22?11 48
Review Problems

51. Find x correct to one decimal place.
y = 25
28.9 49
Review Problems

52. The angle of elevation to the top of a particular skyscraper in New York is found to be 12° from the ground at a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper.
1459 ft 50
Review Problems

53. A man is lying on the beach, flying a kite
A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and estimates the angle of elevation of the kite to be 55° . If the string is 470 ft long, how high is the kite above the ground?
385 ft 51
Review Problems

54. A water tower is located x = 350 ft from a building (see the figure)
A water tower is located x = 350 ft from a building (see the figure). From a window in the building it is observed that the angle of elevation to the top of the tower is 39° and the angle of depression to the bottom of the tower is 25° . How tall is the tower (t)? How high is the window (w)?
t = 447 ft;
w = 163 ft 52
Review Problems

55. When the moon is exactly half full, the earth, moon, and sun form a right angle (see the illustration). At that time the angle formed by the sun, earth, and moon is measured to be If the distance from the earth to the moon is mi, estimate the distance from the earth to the sun.
53,858,204 mi 53
Review Problems

56. From a satellite 500 mi above the earth, it is observed that the angle formed by the vertical and the line of sight to the horizon is Use this information to find the radius of the earth.
3300 mi 54
Review Problems

57. A winch of radius 3 ft is used to lift heavy loads
A winch of radius 3 ft is used to lift heavy loads. If the winch makes 7 revolutions every 15 s, find the speed at which the load is rising.
8.796 55
Review Problems

58. Find the side labeled x. State your answer correct to five decimal places. 56
Review Problems

59. Find the side labeled x. State your answer correct to five decimal places. 57
Review Problems

60. Find x correct to one decimal place.
108.9 58
Review Problems

61. 59 Review Problems A 66-ft tree casts a shadow that is 110 ft long.
  What is the angle of elevation of the sun? Please give the answer to one decimal place.
31.0° 59
Review Problems

62. An airplane is flying at an elevation of 5900 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 52 and to the other is How far apart are the cars? Please round the answer to the nearest foot.
9387 ft 60
Review Problems

63. 61 Review Problems 44° Solve the right triangle.
(a) Find b. Please give the answer to two decimal places.
(b) Find r. Please give the answer to two decimal places.
(c) Find .
30.03
41.75
44° 61
Review Problems

64. 62 Review Problems 13.53 41.66 Solve the right triangle.
(a) Find a. Please give the answer to two decimal places.
(b) Find b. Please give the answer to two decimal places.
(c) Find B. Give your answer in radians.
13.53
41.66 62
Review Problems

65. Find the exact value for each trigonometric function.
(a) sec 120°
(b) tan 390°
(c) cos 315° –2 63
Review Problems

66. To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 34 . One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 37 .
Estimate the height of the mountain. Please round the answer to the nearest foot.
6430 64
Review Problems

67. An airplane is flying at an elevation of 5900 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 52 and to the other is 51 .
How far apart are the cars? Please round the answer to the nearest foot.
9387 65
Review Problems

68. Find the exact value of the expression.66
Review Problems

69. Find the exact value of the expression.67
Review Problems

70. Find the exact value of the expression.68
Review Problems

71. Answers

72. Answers

73. Answers

74. Answers

75. Answers

76. Answers

77. 33.51 11
28.9
1459 ft
385 ft
t = 447 ft; w = 163
53,858,204 mi
3300 mi
8.796 -1 1
12°
-450°
Answers

78. 108.9
31.0°
9387 ft
44°
30.03
41.75
13.53
41.66 –2
6430
9387
Answers