Precalculus Unit 4 Review

Part I: No Calculator

Evaluate and simplify.

1. 2436'47" 15 32'26"+ 2. 90 12 42'30" 3. 13 24 '10"

2

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.

4. 245 5. 5

12

Find the angle with the smallest possible positive measure that is coterminal with the given angle.

6. 932 7. 8

3

Convert the angle to radians. Leave as a multiple of .

8. 210 9. 72 10. 135 11. 15

Convert the radian measure to degree measure.

12. 2

3

13.

4

9

14.

11

6

15.

7

5

Sketch each angle in standard position and state the quadrant in which the terminal side lies.

16. 160 17. 1568 18. 13

8

19.

22

5

Given that is an angle in standard position whose terminal side contains the given point, provide the

exact value of sin , cos , tan , csc , sec , and cot .

20. ( )4, 7 21. ( )2,6 22. ( )6, 8 23. ( )5,12

Find the exact value of the following expressions without using a calculator.

24. 2

sin3

25.

5tan

6

26. cos 225 27. sec 270

28. 3

csc4

29. cot 330 30. ( )sin 60 31.

5cos

3

32. ( )tan 45 33. 7

sec6

34. ( )csc 270 35. ( )cot

Evaluate each expression without using a calculator. Give the result in degrees.

36. ( )1sin 1 37. 1

arccos2

38. 11

tan3

Evaluate each expression without using a calculator. Give the result in radians.

39. 2

arcsin2

40. 13

cos2

41. ( )arctan 1

Find the values of the other five trigonometric functions based on the information given.

42. 8

cos17

= and sin 0.> 43. 4

sin5

= and cos 0.<

44. cot 7= and is in quadrant IV 45. 8

csc5

= and is in quadrant II

Graph each function. Determine the amplitude, period, frequency, phase shift, and vertical shift.

46. 2cos 2 12

y x

= +

47. 3sin 2 16

y x

= +

Graph each function. Determine the period, frequency, phase shift, vertical shift, and the equations of the

asymptotes.

48. csc 12

y x

= + 49. 4sec 3

2

y x

= + 50.

3tan

4 4y x

=

51.

1cot 1

2y x=

Find the equation for the curve in its final position:

52. The graph of ( )siny x= is shifted 4 to the left, stretched by a factor of 3, translated 5 units up, then

reflected in the x-axis.

Find an equation for the function in the graph in the requested form.

53. ( )siny a b x c d= + 54. ( )cosy a b x c d= +

55. The voltage E in an electrical circuit is given by ( )5.2cos 20 ,E t= where t is the time measured in

seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one

second.)

Part II: Calculator

Convert the angle to decimal degrees.

56. 105 24' 57. 23 15'54"

Convert the angle to degrees, minutes, seconds (DMS) form.

58. 31.45 59. 123.815

Find the length of the arc intercepted by the given central angle in a circle of radius r.

60. , 12 ft4

r= = 61. 43, 26.1 m r= =

Find the radius of a circle with central angle intercepting an arc of length s.

62. 57, 17 m s= = 63. , 15 ft3

s= =

Find the area of a sector with the given central angle in a circle of radius r.

64. 2

, 16 ft3

r= = 65. 240 , 8.4 in r= =

Solve each problem.

66. The minute hand of a clock is 5 inches long. What distance does its tip move in 40 minutes?

67. A sensor light installed on the edge of a home can detect motion for a distance of 54 ft. in front of it and with a range of motion of 197. Over what area will the sensor detect motion and become illuminated?

Solve each problem.

68. An engine is turning over at 2300 rpm. Express this angular velocity in rad/min.

69. A wheel with a 20-inch diameter is turning at the rate of 45 revolutions per minute. To the nearest foot per second, what is the linear velocity of a point on the rim?

70. Find the angular velocity in radians per second and the linear velocity in miles per hour for a point on the edge of a 12-in.-diameter record spinning at 1

333 rev/min.

71. A point on the edge of a 16-inch lawnmower blade is rotating at 120 mph. What is the angular velocity of the lawnmower blade in radians per second?

Solve the right triangle with the given sides and angles.

72. 2, 3a b= = 73. 34.6, 9.4 c= = 74. 3.2, 21.3a = = 75. 3, 7a c= =

Solve the problem.

76. A 41-m guy wire is attached to the top of a 34.6-m antenna and to a point on the ground. How far is the point on the ground from the base of the antenna, and what angle does the guy wire make with the ground?

77. From a boat on the lake, the angle of elevation of the top of a cliff is 2117'. If the base of the cliff is 432 feet from the boat, how high is the cliff (to the nearest foot)?

78. The chairlift at a ski resort has a vertical rise of 2458 ft. If the length of the ride is 1.6 miles, what is the average angle of elevation of the lift?

79. At an altitude of 1700 feet, the engine on a small plane fails. What angle of depression is needed to reach an airport runway that is 2.4 miles away by land?

80. A tourist spots a rock climber quite high up at Devils Tower in Wyoming. The angle of elevation of the climber is 36. From a point that is 100 ft. closer to the climber, the angle of elevation is 44. What is the

height of the climber, to the nearest foot?