Math 1316 General Review for Trigonometry Last Updated 08/15/2014

MULTIPLE CHOICE. Choose the one alternative that bestcompletes the statement or answers the question.

Find the measure of each angle in the problem.1. Supplementary angles with measures 3x + 8

and 2x - 3 degreesa. 83° and 97° b. 98° and 82°c. 128° and 52° d. 113° and 67°

2. Complementary angles with measures 4x and5x - 9 degrees

a. 84° and 96° b. 44° and 46°c. 11° and 79° d. 46° and 44°

3. A wheel makes 396 revolutions per minute.How many revolutions does it make persecond?

a. 13.2 revolutions per secondb. 2376 revolutions per secondc. 3.96 revolutions per secondd. 6.6 revolutions per second

4. A wheel is rotating 720 times per minute.Through how many degrees does a point on

the edge of the wheel move in 14

seconds?

a. 72° b. 270°c. 1080° d. 810°

Suppose that is in standard position and the given pointis on the terminal side of . Give the exact value of theindicated trig function for .

5. (18, 24); Find csc .

a. 54

b. 34

c. 53

d. 43

An equation of the terminal side of an angle in standardposition is given along with a restriction on x. Find theindicated trigonometric function value of . Do not use acalculator.

6. -3x + y = 0, x 0; Find sin .

a. 1010

b. 3 1010

c. 3 d. 13

7. 4x + 5y = 0, x 0; Find csc .

a. 54

b. -54

c. 414

d. -45

Evaluate the expression.8. sin 450°

a. 0 b. 12

c. 1 d. Undefined

9. cos(-90°)

a. 32

b. 0

c. -1 d. Undefined

Use the appropriate identity to find the indicated functionvalue. Rationalize the denominator, if applicable. If thegiven value is a decimal, round your answer to threedecimal places.

10. cot , given that tan = 0.3474a. 2.879 b. 2.872c. 2.893 d. 2.886

11. tan , given that cot =5

8

a. 5 58

b. 85

c. 55

d. 8 55

Use the fundamental identities to find the value of thetrigonometric function.

12. Find tan , given that sin =34

and is in

quadrant II.

a. -7

9b. -

3 77

c. -32

d. 54

1

13. Find sec , given that tan =34

and is in

quadrant I.

a. -32

b. 3 77

c. 54

d. -7

9

14. Find sec , given that tan = 0.57735027 and is in quadrant I.

a. -1.1547005 b. -1.2559261c. 1.2559261 d. 1.1547005

15. Find tan , given that cos = -0.58778525 and is in quadrant II.

a. 1.9734303 b. 1.3763819c. -1.9734303 d. -1.3763819

16. Find the exact value of x in the figure.

14

a. 5 3 b. 7 3c. 7 6 d. 8 3

17. Find the exact value of x in the figure.

28

x

a. 14 3 b. 28 33

c. 28 63

d. 14 6

Find the exact value of the expression.18. cos 150°

a. 32

b. 22

c. -3

2d. -

22

19. sec 210°

a. - 2 b. 2

c. 2 33

d. -2 3

3

20. cos (-2190°)

a. -3

2b. 3

2

c. 12

d. -12

Solve the problem.21. On a sunny day, a flag pole and its shadow

form the sides of a right triangle. If thehypotenuse is 40 meters long and the shadowis 32 meters, how tall is the flag pole?

a. 72 m b. 64 mc. 51 m d. 24 m

2

22. To measure the width of a river, a surveyorstarts at point A on one bank and walks 74 feetdown the river to point B. He then measuresthe angle ABC to be 23°32'12''. Estimate thewidth of the river to the nearest foot. See thefigure below.

C

A 74 ft B

a. 32 ft b. 68 ftc. 30 ft d. 170 ft

23. An airplane travels at 180 km/h for 5 hr in adirection of 289° from Greenville. At the endof this time, how far west of Greenville is theplane (to the nearest kilometer)?

a. 310 km b. 952 kmc. 293 km d. 851 km

24. A ship travels 99 km on a bearing of 35°, andthen travels on a bearing of 125° for 129 km.Find the distance from the starting point to theend of the trip, to the nearest kilometer.

a. 81 km b. 57 kmc. 163 km d. 228 km

25. Find h as indicated in the figure. Round to thenearest foot.

24.9° 59.3°

102 ft

a. 68 ft b. 70 ftc. 65 ft d. 62 ft

26. The angle of elevation from a point on theground to the top of a tower is 38° 19 . Theangle of elevation from a point 145 feet fartherback from the tower is 26° 41 . Find the heightof the tower. Round to the nearest foot.

a. 2002 ft b. 196 ftc. 211 ft d. 200 ft

Find the exact value without using a calculator.

27. csc 53

a. - 3 b. - 2

c. -12

d. -2 3

3

28. sec -54

a. -2 b. - 2

c. -2 3

3d. 2

2

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimalplace.

29. r = 15.95 ft; =29

radians

a. 3.5 ft b. 1.7 ftc. 0.9 ft d. 5.2 ft

30. r = 116.15 in.; = 162°a. 328.4 in. b. 164.2 in.c. 656.8 in. d. 104.5 in.

31. Find the distance between City E, 43° N andCity F, 74° S. (Round to the nearest kilometer.)

a. 3455 km b. 13,069 kmc. 13,077 km d. 3463 km

Assume that the cities lie on the same north-south lineand that the radius of the earth is 6400 km.

32. Find the latitude of Winnipeg, Canada ifWinnipeg and Austin, TX, 30°N, are 2234 kmapart.

a. 20°N b. 70°Nc. 50°N d. 60°N

3

33. A wheel with a 38-inch radius is marked attwo points on the rim. The distance betweenthe marks along the wheel is found to be 14inches. What is the angle (to the nearest tenthof a degree) between the radii to the twomarks?

a. 19.1° b. 23.1°c. 17.1° d. 21.1°

34. Two wheels are rotating in such a way that therotation of the smaller wheel causes the largerwheel to rotate. The radius of the smallerwheel is 3.1 centimeters and the radius of thelarger wheel is 17.4 centimeters. Through howmany degrees (to the nearest hundredth of adegree) will the larger wheel rotate if thesmaller one rotates 140°?

a. 24.94° b. 25.94°c. 26.94° d. 24.84°

Find the area of a sector of a circle having radius r andcentral angle . If necessary, express the answer to thenearest tenth.

35. r = 23.0 ft, =3

radians

a. 1107.9 ft2 b. 50.4 ft2

c. 554.0 ft2 d. 24.1 ft2

36. r = 19.5 mi, = 151°a. 1002.1 mi2 b. 25.7 mi2

c. 501.1 mi2 d. 33.9 mi2

37. Find the measure (in radians) of a central angleof a sector of area 46 square inches in a circle ofradius 7 inches. Round to the nearesthundredth.

a. 2.82 radians b. 0.94 radiansc. 3.76 radians d. 1.88 radians

38. A pendulum swings through an angle of 19°each second. If the pendulum is 17 cm inlength and the complete swing from right toleft lasts 2 seconds, what area is covered byeach complete swing? Round to the nearesthundredth.

a. 47.92 cm2 b. 191.67 cm2

c. 95.84 cm2 d. 5.64 cm2

Find the exact circular function value.

39. tan -56

a. 3 b. - 3

c. 32

d. 33

40. csc -23

a. -12

b. -2 3

3

c. - 2 d. - 3

The figure shows an angle in standard position with itsterminal side intersecting the unit circle. Evaluate theindicated circular function value of .

41. Find sin .

-513

, 1213

a. 512

b. 1213

c. -513

d. -1213

4

42. Find csc .

725

, - 2425

a. 2524

b. 247

c. -2524

d. -257

43. sec 0.1943a. 0.1931 b. 0.1968c. 0.9812 d. 1.0192

Use a table or a calculator to evaluate the function. Roundto four decimal places.

44. csc 0.2391a. 0.2368 b. 0.9716c. 4.2225 d. 1.0293

Suppose an arc of length s lies on the unit circle x2 + y2 =

1, starting at point (1, 0) and terminating at the point (x, y).Use a calculator to find the approximate coordinates (x, y).Round coordinates to four decimal places whenappropriate.

45. s = 7.6a. (0.9679, 0.2513)b. (-0.2513, -0.9679)c. (-0.2513, 0.9679)d. (0.2513, 0.9679)

Find the exact values of s in the given interval that satisfythe given condition.

46. [0, 2 ); tan2 s = 13

a.6

, 76

b.3

, 23

, 43

, 53

c.3

, 43

d.6

, 56

, 76

, 116

47. [- , ); 2 cos2 s = 1

a.4

, 4

, 4

, 74

b. -23

, -3

, 3

, 23

c. -74

, -4

, -4

, -4

d. -34

, -4

, 4

, 4

5

48. Let angle POQ be designated . Angles PQRand VRQ are right angles. If = 45°, find theexact length of OQ.

a. 2 b. 1

c. 0 d. 22

49. Let angle POQ be designated . Angles PQRand VRQ are right angles. If = 80°, find thelength of OQ accurate to four decimal places.

a. 0.1736 b. 0.9848c. 5.7588 d. 5.6713

50. Let angle POQ be designated . Angles PQRand VRQ are right angles. If = 27°, find thelength of OU accurate to four decimal places.

a. 2.2027 b. 0.8910c. 1.1223 d. 0.4540

51. =6

radian per min, t = 13 min

a. 78 radians b. 136

radians

c.78

radian d. 613

radians

Use the formula =t

to find the value of the missing

variable. Give an exact answer unless otherwise indicated.52. = 9.2302 radians per min, = 13.09 radians

(Round to four decimal places whennecessary.)

a. 1.4182 min b. 0.7051 minc. 22.3202 min d. 120.8233 min

Use the formula v = r to find the value of the missingvariable. Give an exact answer unless otherwise indicated.

53. v = 16 ft per sec, r = 3.3 ft (Round to fourdecimal places when necessary.)

a. 0.952 radian per secb. 5.0929 radians per secc. 0.2063 radian per secd. 4.8485 radians per sec

6

Use the formula s = r t to find the value of the missingvariable. Give an exact answer.

54. s =3

m, r = 7 m, t = 32 sec

a.672

radian per sec

b. 672 radians per sec

c. 2132

radians per sec

d. 3221

radian per sec

55. A wheel is rotating at 8 radians/sec, and thewheel has a 38-inch diameter. To the nearestfoot, what is the speed of a point on the rim inft/min?

a. 755 ft/min b. 765 ft/minc. 760 ft/min d. 750 ft/min

56. A wheel with a 22-inch diameter is turning atthe rate of 58 revolutions per minute. To thenearest inch, what is the speed of a point onthe rim in in./min?

a. 4055 in./min b. 4009 in./minc. 4062 in./min d. 4016 in./min

Graph the function.

57. y = sin 14

x

a.

b.

c.

7

d.

58. y = cos 13

x

a.

b.

c.

d.

8

59. y = 2 + sin x +3

a.

b.

c.

d.

Graph the function over a one-period interval.60. y = 4 + 4 sin(x - )

a.

9

b.

c.

d.

SHORT ANSWER. Write the word or phrase that bestcompletes each statement or answers the question.

Verify that each equation is an identity.

61. sec + tan = cos 1 - sin

62. sec - 1tan

=tan

sec + 1

63. (sec + tan )2 =1 + sin 1 - sin

MULTIPLE CHOICE. Choose the one alternative that bestcompletes the statement or answers the question.

Use Identities to find the exact value.64. cos (-75°)

a. 2 - 6 b. 6 - 24

c. 2 - 64

d. - 6 - 2

65. cos 255°

a. 6 - 2 b. 2 - 6

c. 6 - 24

d. 2 - 64

66. cos 12

a. 2 - 64

b. - 6 - 24

c. 6 + 24

d. 6 - 24

67. Find cos(s + t) given that cos s = 13

, with s in

quadrant I, and sin t = -12

, with t in quadrant

IV.

a. 3 + 2 26

b. 3 - 2 26

c. 2 6 - 16

d. 2 6 + 16

68. Find cos(s - t) given that cos s = -45

, with s in

quadrant II, and cos t = 513

, with t in

quadrant IV.

a. 5665

b. 1665

c. - 5665 d. -

1665

10

69. sin 15°

a. 6 + 24

b. 6 - 24

c. - 6 - 24

d. - 6 + 24

70. tan 75°a. - 3 - 2 b. 3 - 2c. - 3 + 2 d. 3 + 2

71. sin 1112

a. 6 + 24

b. - 6 - 24

c. 6 - 24

d. - 6 + 24

72. sin 712

a. 2 - 64

b. 2 + 64

c. 6 - 24

d. 2 + 2 64

73. tan 345°a. 3 + 2 b. - 3 + 2c. - 3 - 2 d. 3 - 2

Use a sum or difference identity to find the exact value.

74. sin 712

a. 6 + 24

b. 3 + 12

c. 6 - 24

d. 12

75. tan 1112

a. -2 - 3 b. 2 - 3c. -2 + 3 d. 2 + 3

Find the exact value of the expression using the providedinformation.

76. Find sin(s - t) given that cos s = 13

, with s in

quadrant I, and sin t = -12

, with t in

quadrant IV.

a. 3 + 2 26

b. 3 - 2 26

c. 2 6 - 16

d. 2 6 + 16

77. Find sin(s + t) given that cos s = -513

, with s in

quadrant II, and sin t = 1517

, with t in

quadrant II.

a. -21221

b.21221

c. - 171221 d. 171

221

Use identities to find the indicated value for each anglemeasure.

78. sin =35

, cos > 0 Find cos(2 ).

a. 2425

b.15

c.725 d. -

725

79. sin = -45

, 2

< < 2 Find cos(2 ).

a. -725

b. -2425

c. 2425

d. 725

Find the exact value by using a half-angle identity.80. sin 22.5°

a. -12

2 + 2 b. 12

2 - 2

c. 12

2 + 2 d. -12

2 - 2

11

81. cos 75°

a. 12

2 - 3 b. -12

2 + 3

c. -12

2 - 3 d. 12

2 + 3

82. tan 75°a. -2 - 3 b. 2 - 3c. -2 + 3 d. 2 + 3

83. sin 512

a. -12

2 + 3 b. 12

2 + 3

c. -12

2 - 3 d. 12

2 - 3

84. cos 512

a. -12

2 + 3 b. 12

2 - 3

c. -12

2 - 3 d. 12

2 + 3

85. tan 165°a. 2 + 3 b. -2 - 3c. -2 + 3 d. 2 - 3

Give the exact value of the expression.

86. cos arcsin 35

+ arccos 32

a. 2 3+25

b. 4 3-310

c. -25 3-48100

d. 4 3+310

Solve the equation for exact solutions over the interval [0,2 ).

87. cos2x + 2 cos x + 1 = 0

a. } b.2

, 32

c. {2 } d.4

, 74

88. 2 sin2x = sin x

a.3

, 23

b.6

, 56

c.2

, 32

, 3

, 23

d. 0, , 6

, 56

Solve the equation (x in radians and in degrees) for allexact solutions where appropriate. Round approximateanswers in radians to four decimal places and approximateanswers in degrees to the nearest tenth.

89. 2 sin2 x + sin x = 1

a.6

+ 2n , 56

+ 2n

b.2

+ 2n , 56

+ 2n , 32

+ 2n

c.6

+ 2n , 32

+ 2n

d.6

+ 2n , 56

+ 2n , 32

+ 2n

90. 3 cos2 + 2 cos = 1

a. {51.8° + 360°n, 128.2° + 360°n}b. {70.5° + 360°n, 180° + 360°n, 289.5° +

360°n}c. {49.8° + 360°n, 130.2° + 360°n, 229.8° +

360°n, 310.2° + 360°n}d. {103.2° + 360°n, 145.2° + 360°n, 283.2° +

360°n, 325.2° + 360°n}

Solve the equation for solutions in the interval [0, 2 ).

91. sin 4x = 32

a.12

, 6

, 23

, 712

, 76

, 1312

, 53

, 1912

b. {0}

c.4

, 54

d. 0, 4

,

12

92. cos 2x = 2 - cos 2xa.

b.4

, 34

, 54

, 74

c.8

, 98

, 78

, 158

d. 0, 23

, , 43

Solve the equation for solutions in the interval [0°, 360°).Round to the nearest degree.

93. sin 2 = cos a. {15°, 165°, 195°, 345°}b. {30°, 90°, 150°, 270°}c. {0°, 120°, 180°, 240°}d. {105°, 165°, 285°, 345°}

Solve the equation for solutions over the interval [0, 2 ).Write solutions as exact values or to four decimal places,as appropriate.

94. sin x2

+ cos x2

= 2

a. {0 , } b. }

c.4

d.2

95. tan 2x + sec 2x = 2a. {0.6435, 6.9267} b. {2.2143, 8.4975}c. {1.1072, 4.2488} d. {0.3218, 3.4634}

Solve the equation for exact solutions.96. arcsin 2x + 2 arccos x =

a. 1 b. -3

2, 3

2

c. 0 d. -3

4, 3

4

97. arcsin x + 2 arctan x =

a. 0 b. -3

2, 3

2

c. -3

4, 3

4d. 1

98. sin-1x + tan-1x = 0

a. -3

4, 3

4b. 0

c. -3

2, 3

2d. 1

Solve the triangle. Round to the nearest tenth whennecessary or to the nearest minute as appropriate.

99. B = 40.9°C = 114.5°b = 17.8

a. A = 22.6°, a = 26.7, c = 13.3b. A = 24.6°, a = 13.3, c = 26.7c. A = 22.6°, a = 24.7, c = 11.3d. A = 24.6°, a = 11.3, c = 24.7

100. A = 37°10'B = 26°10'a = 36.2

a. C = 117°40', b = 53.5, c = 26.4b. C = 117°40', b = 26.4, c = 53.5c. C = 116°40', b = 26.4, c = 53.5d. C = 116°40', b = 53.5, c = 26.4

Find the area of triangle ABC with the given parts. Roundto the nearest tenth when necessary.

101. A = 38.2°b = 14.2 in.c = 4.4 in.

a. 26.6 in.2 b. 24.6 in.2

c. 17.3 in.2 d. 19.3 in.2

102. A = 25°50'b = 17.5 mc = 8.9 m

a. 67.8 m2 b. 33.9 m2

c. 17 m2 d. 69.8 m2

Solve the problem.103. Two tracking stations are on the equator 173

miles apart. A weather balloon is located on abearing of N 42°E from the western station anda bearing of N 12°E from the eastern station.How far, to the nearest mile, is the balloonfrom the western station? Round to the nearestmile.

a. 271 mi b. 280 mic. 338 mi d. 347 mi

13

104. An airplane is sighted at the same time by twoground observers who are 2 miles apart andboth directly west of the airplane. They reportthe angles of elevation as 13° and 20°. Howhigh is the airplane? Round to the nearesthundredth of a mile.

a. 1.92 mi b. 1.26 mic. 0.68 mi d. 0.45 mi

Find the missing parts of the triangle.105. B = 19.7°

b = 12.80a = 18.99If necessary, round angles to the nearest tenthand side lengths to the nearest hundredth.

a. A1 = 30.01°, C1 = 130.29°, c1 = 28.96;A2 = 149.99°, C2 = 10.31°, c2 = 6.8

b. A = 149.99°, C = 10.31°, c = 6.8c. no such triangled. A = 30.01°, C = 130.29°, c = 28.96

106. C = 35°30'a = 18.76c = 16.15If necessary, round side lengths to the nearesthundredth.

a. A1 = 42°25', B1 = 102°05', b1 = 27.2;A2 = 137°35', B2 = 6°55', b2 = 3.35

b. A = 42°25', B = 102°05', b = 25.19c. no such triangled. A1 = 102°05', B1 = 42°25', b1 = 17.52;

A2 = 6°55', B2 = 137°35', b2 = 26.19

Find the missing parts of the triangle. Round to thenearest tenth when necessary or to the nearest minute asappropriate.

107. C = 106.2°a = 6.3 kmb = 8.1 km

a. c = 11.6 km, A = 31.4°, B = 42.4°b. c = 17.4 km, A = 29.4°, B = 44.4°c. c = 14.5 km, A = 33.4°, B = 40.4°d. No triangle satisfies the given conditions.

108. C = 118.5°a = 7.3 mb = 11.7 m

a. c = 22.3 m, A = 20.8°, B = 40.7°b. c = 16.5 m, A = 22.8°, B = 38.7°c. No triangle satisfies the given conditions.d. c = 19.4 m, A = 24.8°, B = 36.7°

109. a = 18.9 cmb = 15.7 cmc = 14.9 cm

a. 123 cm2 b. 117 cm2

c. 114 cm2 d. 120 cm2

110. Two ships leave a harbor together traveling oncourses that have an angle of 129° betweenthem. If they each travel 502 miles, how farapart are they (to the nearest mile)?

a. 1812 mi b. 432 mic. 40 mi d. 906 mi

111. Two airplanes leave an airport at the sametime, one going northwest (bearing 135°) at 417mph and the other going east at 338 mph.How far apart are the planes after 4 hours (tothe nearest mile)?

a. 2193 mi b. 2793 mic. 698 mi d. 2325 mi

Find the magnitude and direction angle (to the nearesttenth) for each vector. Give the measure of the directionangle as an angle in [0,360°].

112. 2, 2a. 2 2; 45° b. 2 2; 225°c. 2; 225° d. 4; 45°

113. -6 2, -6 2a. 12 2; 135° b. 12; 225°c. 12; 45° d. 24; 45°

Two forces act at a point in the plane. The angle betweenthe two forces is given. Find the magnitude of theresultant force.

114. forces of 28.1 and 43.2 lb, forming an angle of76.5°(round to the nearest pound)

a. 2089 lb b. 46 lbc. 57 lb d. 71 lb

14

Find the dot product for the pair of vectors.115. 10, -12 , -8, -4

a. 48 b. -32c. -80 d. -128

116. 5i - 4j, 8i + ja. 36 b. -27c. 44 d. 0

Find the angle between the pair of vectors to the nearesttenth of a degree.

117. 3, 7 , 9, -6a. 40.3° b. 50.3°c. 100.5° d. 110.5°

118. 9i - 5j, 2i - 9ja. 114.4° b. 48.4°c. 44.7° d. 126.9°

Determine whether the pair of vectors is orthogonal.119. -2, 6 , -8, -5

a. Yes b. No

120. 3i - 2j, -8i - 12ja. Yes b. No

121. Two forces of 498 newtons and 257 newtonsact at a point. The resultant force is 578newtons. Find the angle between the forces.

a. 85.5° b. 80.3°c. 94.5° d. 164.0°

122. A force of 621 lb is required to pull a boat up aramp inclined at 19° with the horizontal. Howmuch does the boat weigh?

a. 2494 lb b. 587 lbc. 1907 lb d. 602 lb

123. Two boats are pulling a disabled vessel towardthe landing dock with forces of 950 lb and 940lb. The angle between the forces is 21.8°. Findthe direction and magnitude of the equilibrant.

a. 1856 lb at an angle of 10.8° with the950-lb force

b. 1856 lb at an angle of 79.2° with the940-lb force

c. 186 lb at an angle of 169.2° with the950-lb force

d. 1856 lb at an angle of 169.2° with the950-lb force

Find the product. Write the product in rectangular form,using exact values.

124. [4(cos 30° + i sin 30°)] [6(cos 330° + i sin 330°)]a. 12 3 + 12i b. -12 + 12 3ic. 24 d. 24i

Find the quotient and write in rectangular form. Firstconvert the numerator and denominator to trigonometricform.

125. 5(cos 200° + i sin 200°)4(cos 50° + i sin 50°)

a. -5 3

8+

58

i b. -2 + 2 3i

c. -12

+3

2i d. -10 + 10 3i

126. 8(cos 90 + i sin 90)3(cos 30 + i sin 30)

a. 8 + 8 3i b. 1 + 3i

c. 43

+4 3

3i d. 5

2+

5 32

i

Find the given power. Write answer in rectangular form.127. (- 3 + i)6

a. 64i b. 64 - 64 3ic. -64 3 + 64i d. -64

128. -12

-3

2i

10

a. 12

+3

2i b. 1

2-

32

i

c. -12

+3

2i d. -

12

-3

2i

Find all specified roots.129. Cube roots of 1.

a. 1, 12

+3

2i, - 1

2+

32

i

b. 1, - 12

+3

2i, - 1

2-

32

i

c. 1, 12

-3

2i, - 1

2-

32

i

d. -1, 1

15

130. Cube roots of i.

a. 32

+12

i, - 32

+12

i, i

b. 32

-12

i, - 32

-12

i, i

c. 32

-12

i, - 32

-12

i, -i

d. 32

+12

i, - 32

+12

i, -i

16

Answer KeyTestname: GENERAL TRIG REVIEW

1. d2. b3. d4. c5. a6. b7. c8. c9. b

10. a11. d12. b13. c14. d15. d16. b17. c18. c19. d20. b21. d22. a23. d24. c25. c26. d27. d28. b29. b30. a31. b32. c33. d34. a35. c36. c37. d38. c39. d40. b41. b42. c43. d44. c45. d46. d47. d48. d49. a50. a

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Answer KeyTestname: GENERAL TRIG REVIEW

51. b52. a53. d54. a55. c56. b57. b58. b59. a60. b

61. sec + tan = 1cos

+sin cos

=1 + sin

cos =

1 + sin cos

·1 - sin 1 - sin

=1 - sin2

cos (1 - sin )=

cos2cos (1 - sin )

=cos

1 - sin

62. sec - 1tan

=sec - 1

tan ·

sec + 1sec + 1

=sec2 - 1

tan (sec + 1)=

tan2tan (sec + 1)

=tan

sec + 1

63. (sec + tan )2 = sec2 + 2 sec tan + tan2 = 1cos2

+2 sin cos2

+sin2

cos2=

1 + 2 sin + sin2

cos2=

(1 + sin )2

1 - sin2=

(1 + sin )2(1 - sin )(1 + sin )

=1 + sin 1 - sin

64. b65. d66. c67. a68. c69. b70. d71. c72. b73. d74. a75. c76. d77. c78. c79. a80. b81. a82. d83. b84. b85. c86. b87. a88. d89. d90. b91. a92. c93. b

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Answer KeyTestname: GENERAL TRIG REVIEW

94. d95. d96. c97. d98. b99. d

100. c101. d102. b103. c104. b105. a106. a107. a108. b109. c110. d111. b112. a113. b114. c115. b116. a117. c118. b119. b120. a121. a122. c123. d124. c125. a126. c127. d128. d129. b130. d

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