1. T RIGONOMETRY Final Review

2. 1. A PPROXIMATE SEC 320°.77.90 1.1 1.3

3. T RY AGAIN

4. E XCELLENT !

5. 2. I F SEC  =2 FIND TAN . √3/2 ½ √3 2

6. T RY AGAIN

7. F ABULOUS !

8. 3. F IND TAN 7 Π /4.10 -.10 1

9. T RY A GAIN

10. G REAT J OB !

11. 4. F IND A POSITIVE AND NEGATIVE ANGLE COTERMINAL TO 5 Π /3 ( IN RADIANS ). -11π/3 and π/3 -π/3 and 11π/3 -11π/3 and 11π/3 -π/3 and π/3

12. T RY A GAIN

13. W AY TO G O !

14. 5. F IND THE REFERENCE ANGLE FOR 13 Π /6. π/6 or 30° π/3 or 60° -π/6 or -30° -π/3 or -60°

15. T RY A GAIN

16. R OCK ON !

17. 6. F IND ALL VALUES BETWEEN 0 AND 360° WHERE SIN  =-1/2 150° and 210° 240° and 320° 210° and 330° 150° and 330°

18. T RY AGAIN

19. W OW !

20. 7. F IND THE APPROXIMATE ARC LENGTH IF THE CENTRAL ANGLE IS 40° AND THE RADIUS OF THE CIRCLE BEING INTERCEPTED IS 5 UNITS. 1.75 3.49 5.25 200

21. T RY AGAIN !

22. S UPER !

23. 8. a=4 b=3 and c=5. Find A..64 degrees.93 degrees 36.9 degrees 53.1 degrees

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25. Y OU ROCK !

26. 9. B=34°20’ C=90° and c=8. Find b. 1.78 4.5 6.6 14.8

27. T RY AGAIN !

28. M AGNIFICENT !

29. 10. A=32° C=90° and b=5. Find a. 2.00 3.12 4.24 8.00

30. T RY AGAIN !

31. M ARVELOUS !

32. 11. A=40° B=80° and c=4. Find b. 1.39 2.97 4.55 6.13

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34. O UTSTANDING !

35. 12. S IMPLIFY TAN A COS ²A sinAcosA cosAtanA sin²A tan²A

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37. A WESOME !

38. 13. S IMPLIFY SINX + COSXTANX. sinxcosx 2cosx 2tanx 2sinx

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40. H OORAY !

41. 14. S IMPLIFY TANXCSCX sinx cosx secx cotx

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43. G REAT JOB !

44. 15. W HICH ONE IS EQUIVALENT TO 1+ TAN  SEC  1+csc  1+cot  2sin  cos 2sin  cos  sin  +cos 

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46. W AY TO GO !

47. 16. W HICH IS EQUIVALENT TO 1+ SEC ² XSIN ² X csc²x sec²x tan²x cot²x

48. T RY AGAIN !

49. G REAT JOB !

50. 17. F IND THE DOMAIN AND RANGE FOR Y = CSCX Domain: all reals not equal to πk; Range: (-∞,- 1][1,∞) Domain: (-∞,-1][1,∞); Range: all reals not equal to πk Domain: all reals; Range: [-1,1] Domain: all reals not equal to π/2+πk; Range: (- ∞,-1][1,∞)

51. T RY A GAIN !

52. O UTSTANDING !

53. 18. N AME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y = COS (2  + Π ) Amplitude: 2, period: π, and phase shift π/2 right Amplitude: 2, period: π/2, and phase shift π/2 left Amplitude: 1, period: π/2, and phase shift π/2 right Amplitude: 1, period: π, and phase shift π/2 left

54. T RY AGAIN !

55. K EEP UP THE GREAT WORK !

56. 19. N AME THE PERIOD AND PHASE SHIFT FOR Y = TAN (  - Π /2) Period π and phase shift π/2 right Period π and phase shift π/2 left Period 2π and phase shift π/2 right Period 2π and phase shift π/2 left

57. T RY AGAIN !

58. R IGHT ON !

59. 20. N AME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y =-3 COS (4 X + Π /2) Amplitude 3, period π/4, and phase shift π/2 left Amplitude 3, period π/4, and phase shift π/8 left Amplitude 3, period π/2, and phase shift π/2 left Amplitude 3, period π/2, and phase shift π/8 left

60. T RY AGAIN !

61. S O PROUD OF YOU !

62. 21. F IND THE AREA OF A CIRCULAR SEGMENT TO THE NEAREST TENTH IF THE MEASURE OF ITS CENTRAL ANGLE IS 220° AND THE MEASURE OF ITS RADIUS IS 8.5 UNITS. 935 units² 138.7 units² 7947.5 units² 10,021.8 units²

63. T RY AGAIN

64. E XCELLENT !

65. 22. F IND ALL VALUES OF X WHERE SIN X = 1. 270° + 360k 180° + 360k 90° +360k 360k

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67. F ABULOUS !

68. 23. E VALUATE COS ( SIN -1 1/2). A SSUME X IS IN QUADRANT 1. √(3)/2 √3 2 √(3)/3

69. T RY AGAIN

70. G REAT J OB !

71. 24. F IND THE VALUES OF X IN THE INTERVAL [-180˚, 180˚] THAT SATISFY THE EQUATION SIN X = -1/2. 30˚ and 150˚ 60˚ and 300˚ -60˚ and -300˚ -30˚ and -150˚

72. T RY AGAIN

73. W AY TO G O !

74. 25. E VALUATE COS ( TAN -1 1) + SIN ( TAN -1 √3) ( X IS IN Q UADRANT I) 1 + √(3)/2 2 + √(2)/2 √(2)/2 + √(3)/2 √(3)/3 + √3

75. T RY AGAIN

76. R OCK ON !

77. 26. W RITE AN EQUATION OF THE COSINE FUNCTION WITH AMPLITUDE 5, PERIOD 540˚ AND PHASE SHIFT 135˚ TO THE LEFT. Y= 5 cos (2/3x – л/2) Y= 5 cos (2/3x + л/2) Y= 5 cos (1/2x – л/4) Y= 5 cos (1/2x + л/4)

78. T RY AGAIN

79. W OW !

80. 27. E XPRESS COS 510˚ AS A FUNCTION OF AN ANGLE IN QUADRANT I -cos 30˚ cos 30˚ -cos 60˚ cos 60˚

81. T RY AGAIN

82. G REAT JOB !

83. 28. W HICH EQUATION IS A TRIG IDENTITY ? cos