Trig Question Bank.pdf

Trig Q Bank

Name: Date:

1. In right triangle DEF, m∠E = 90, DE = 8,EF = 15, and FD = 17. What is the value oftanF?

A. 817 B. 15

17 C. 815 D. 15

8

2. In the accompanying diagram of right triangleCAR, m∠A = 90, m∠C = 59, and CR = 15. If ARis represented by c, which equation can be used tofind c?

A. sin 59◦ =c15

B. cos 59◦ =c15

C. tan 59◦ =c15

D. sin 31◦ =c15

3. In ÂBC, m∠A = 25 and m∠C = 90. Whichratio represents tan 65◦?

A.AC

ABB.

AC

BCC.

AB

ACD.

BC

AC

4. In the accompanying diagram of right triangleABC, ∠B is a right angle, AB = 8, BC = 15, andCA = 17.

What ratio is equal to 817?

A. sinA B. sinC C. cosC D. tanA

5. In the accompanying diagram of ÂBC, whichexpression can be used to determine m∠A ?

A. sinA = 1213

B. cosA = 125

C. cosA = 513

D. tanA = 512

page1

6. In the accompanying diagram of righttriangle ABC, m∠C = 90, m∠BAC = 48, AC = x,and CB = 16.3.

Which equation could be used to find the lengthof−−−AC?

A. sin 48 =16.3x

B. cos 48 =x

16.3

C. tan 48 =16.3x

D. tan 48 =x

16.3

7. In the accompanying diagram of righttriangle ABC, legs AC and BC are 12 and 5,respectively, and hypotenuse AB is 13.

What is tan B ?

A. 125 B. 12

13

C. 513 D. 5

12

8. In the accompanying diagram of ^CDE,m∠D = 90◦, m∠C = 28◦, and ED = 15. Whichequation can be used to find CD ?

A. sin 28◦ =15

CD

B. sin 28◦ =CD15

C. tan 28◦ =15

CD

D. tan 28◦ =CD15

9. In right triangle ABC, m∠C = 90, m∠A = 63, andAB = 10. If BC is represented by a, then whichequation can be used to find a ?

A. sin 63◦ =a10

B. a = 10 cos 63◦

C. tan 63◦ =a10

D. a = tan 27◦

10. In the accompanying diagram of righttriangle ABC, the hypotenuse is

−−−AB, AC = 3,

BC = 4, and AB = 5. SinB is equal to

A. sinA B. cosA

C. tanA D. cosB

page2 Trig Q Bank

11. In the accompanying diagram of righttriangle ABC, what is tanC ?

A. 23 B. 3

2

C.√

133 D. 2√

13

12. In the accompanying diagram, m∠C = 90,m∠A = 42, and CA = 10. Which equation can beused to find AB ?

A. tan 42◦ =10

AB

B. tan 42◦ =AB10

C. cos 42◦ =AB10

D. cos 42◦ =10

AB

13. In the accompanying diagram, the legs of righttriangle ABC are 5 and 12 and the hypotenuseis 13.

What is the value of cosA ?

A. 1213 B. 13

5

C. 513 D. 12

5

14. In the accompanying diagram, the legs of righttriangle ABC are 4 and 3, and the hypotenuse is 5.What is the value of tanA ?

A. 43 B. 3

5

C. 45 D. 3

4

15. In the accompanying diagram, what is sinE ?

A. 34 B. 4

3

C. 35 D. 4

5

16. In the accompanying diagram of righttriangle ABC, AB = 10, BC = 8, CA = 6, and ∠Cis a right angle. Which angle of the triangle has acosine equal to 0.8000?

page3 Trig Q Bank

17. In the accompanying diagram of righttriangle ABC, AC = 12, AB = 13, and BC = 5.What is the value of sinA − cosA ?

A. 713

B. − 713

C. 1713

D. − 1713

18. In the accompanying diagram of righttriangle ABC, ∠C is a right angle. Whichequation is valid for ÂBC ?

A. cosA =cb

B. tanA =ba

C. sinA =ac

D. cosB =ab

19. Which equation can be used to find the value of xin the right triangle shown?

A. cos 20◦ =x12

B. sin 20◦ =12

x

C. cos 20◦ =12

x

D. cos 70◦ =x12

20. In right triangle ABC, if m∠C = 90 and sinA = 35 ,

cosB is equal to

A. 35 B. 4

5 C. 34 D. 4

3

21. In ÂBC, m∠C = 90. If AB = 5 and AC = 4,which statement is not true?

A. cosA =4

5B. tanA =

3

4

C. sinB =4

5D. tanB =

5

3

22. The diagram below shows right triangle ABC

Which ratio represents the tangent of ∠ABC?

A.5

13B.

5

12C.

12

13D.

12

5

23. In right triangle ABC shown below, AB = 18.3 andBC = 11.2.

What is the measure of ∠A, to the nearest tenthof a degree?

A. 31.5 B. 37.7 C. 52.3 D. 58.5

page4 Trig Q Bank

24. An 8-foot rope is tied from the top of a pole toa stake in the ground, as shown in the diagrambelow.

If the rope forms a 57◦ angle with the ground,what is the height of the pole, to the nearest tenthof a foot?

A. 4.4 B. 6.7 C. 9.5 D. 12.3

25. As shown in the diagram below, a ladder 5 feetlong leans against a wall and makes an angle of65◦ with the ground. Find, to the nearest tenth ofa foot, the distance from the wall to the base ofthe ladder.

26. Right triangle ABC has legs of 8 and 15 and ahypotenuse of 17, as shown in the diagram below.

The value of the tangent of ∠B is

A. 0.4706 B. 0.5333

C. 0.8824 D. 1.8750

27. A communications company is building a 30-footantenna to carry cell phone transmissions. Asshown in the diagram below, a 50-foot wire fromthe top of the antenna to the ground is used tostabilize the antenna.

Find, to the nearest degree, the measure of theangle that the wire makes with the ground.

28. In ÂBC, the measure of ∠B = 90◦, AC = 50,AB = 48, and BC = 14. Which ratio represents thetangent of ∠A?

A. 1450 B. 14

48 C. 4850 D. 48

14

page5 Trig Q Bank

29. In right triangle ABC, AB = 20, AC = 12, BC = 16,and m∠C = 90. Find, to the nearest degree, themeasure of ∠A.

30. Which equation shows a correct trigonometric ratiofor angle A in the right triangle below?

A. sinA = 1517 B. tanA = 8

17

C. cosA = 1517 D. tanA = 15

8

31. A tree casts a 25-foot shadow on a sunny day, asshown in the diagram below.

If the angle of elevation from the tip of theshadow to the top of the tree is 32◦, what is theheight of the tree to the nearest tenth of a foot?

A. 13.2 B. 15.6 C. 21.2 D. 40.0

32. In the right triangle shown in the diagram below,what is the value of x to the nearest wholenumber?

A. 12 B. 14 C. 21 D. 28

33. In the diagram of ÂBC shown below, BC = 10and AB = 16.

To the nearest tenth of a degree, what is themeasure of the largest acute angle in the triangle?

A. 32.0 B. 38.7 C. 51.3 D. 90.0

page6 Trig Q Bank

34. Which equation could be used to find the measureof one acute angle in the right triangle shownbelow?

A. sinA = 45 B. tanA = 5

4

C. cosB = 54 D. tanB = 5

4

35. The center pole of a tent is 8 feet long, and a sideof the tent is 12 feet long as shown in the diagrambelow.

If a right angle is formed where the center polemeets the ground, what is the measure of angle Ato the nearest degree?

A. 34 B. 42 C. 48 D. 56

36. In the accompanying diagram of right triangleABC, m∠C = 90, AB = 18, and m∠B = 52. Findthe length of to the nearest tenth.

37. In the accompanying diagram of right triangleRUN, m∠U = 90, m∠N = 37, and RN = 21.

What is the length of−−−RU, expressed to the nearest

tenth?

A. 12.6 B. 15.8 C. 16.8 D. 34.9

38. In the accompanying diagram of right triangleABC, a right angle is at C, AB = 26, andm∠A = 27. Find the length of

−−−BC to the nearest

tenth.

page7 Trig Q Bank

39. In right triangle ABC, m∠C = 90, m∠A = 55, andCA = 10. What is the length of

−−−AB to the nearest

integer?

A. 6 B. 14 C. 17 D. 24

40. In right triangle BCD, BD = 12, m∠C = 90, andm∠DBC = 47. Find DC to the nearest tenth.

41. In the diagram below of a unit circle, the ordered

pair (−√

22 , −

√2

2 ) represents the point where theterminal side of θ intersects the unit circle.

What is m∠θ?

A. 45 B. 135 C. 225 D. 240

42. On the unit circle shown in the diagram below,sketch an angle, in standard position, whosedegree measure is 240 and find the exact value ofsin 240◦.

43. In the unit circle shown in the accompanyingdiagram, what are the coordinates of (x, y)?

A.

(−

√3

2,−0.5

)B.

(−0.5,−

√3

2

)

C. (−30,−210) D.

(−

√2

2,−√

2

2

)

page8 Trig Q Bank

44. The accompanying diagram shows unit circle O,with radius OB = 1.

Which line segment has a length equivalent tocos θ?

A.−−−AB B.

−−−CD C.

−−−−OC D.

−−−OA

45. In the accompanying diagram of a unit circle,

the ordered pair(−√

32 ,−

12

)represents the point

where the terminal side of θ intersects the unitcircle.

What is m∠θ?

A. 210 B. 225 C. 233 D. 240

46. In the accompanying diagram, point P(0.6,−0.8)is on unit circle O. What is the value of θ, to thenearest degree?

47. If θ is an angle in standard position and its

terminal side passes through the point(

12 ,√

32

)on

a unit circle, a possible value of θ is

A. 30◦ B. 60◦ C. 120◦ D. 150◦

48. In the accompanying diagram of a unit circle, theordered pair (x, y) represents the point where theterminal side of θ intersects the unit circle.

If x = − 12 , what is one possible value for θ?

A. 60◦ B. 120◦ C. 145◦ D. 150◦

page9 Trig Q Bank


If θ = 150◦, what is the value of x?

A. 1 B. −√

32 C. − 1

2 D. −√

22

50. If θ is an angle in standard position and its

terminal side passes through point (− 12 ,√

32 ) on the

unit circle, then a possible value of θ is

A. 60◦ B. 120◦ C. 150◦ D. 330◦


If θ = 3π4 , what is the value of x ?

A. 1 B. − 12

C. −√

22 D.

√3

2

52. In the accompanying diagram of a unit circle, theordered pair (x, y) represents the point where theterminal side of θ intersects the unit circle. Ifθ = − π3 , what is the value of y ?

A. −√

32

B. −√

22

C. −√

3

D. − 12

53. In the accompanying diagram of a unit circle, theordered pair (x, y) represents the point where theterminal side of θ intersects the unit circle. Ifm∠θ = 120, what is the value of x in simplestform?

A. −√

32 B.

√3

2

C. − 12 D. 1

2

54. In the accompanying diagram of circle O, point Ois the origin, YO = 1, JO = 1, and

−−−−−TOY is a

diameter. If the coordinates of point J are(√2

2 ,√

22

), how many degrees are in the m∠JOY ?

page10 Trig Q Bank

55. In the accompanying diagram, the center ofcircle O is at the origin, radius OB = 1, andm∠AOB = 30. What are the coordinates ofpoint B ?

A.(

12 ,√

32

)B.

(√2

2 ,√

22

)C.

(√3

2 ,12

)D. (1, 1)

56. In the accompanying diagram of circle O,COA is a diameter, O is the origin,

−−−OA = 1, and

m∠BOA = 30. What are the coordinates of B?

A.(

12 ,

√3

2

)B.

(√3

2 ,12

)C.

(√2

2 ,√

22

)D.

(√2

2 ,12

)

57. In the accompanying diagram,−−−PR is tangent to

circle O at R,−−−QS ⊥

−−−0R, and

−−−PR ⊥

−−−OR.

Which measure represents sin θ?

A. SO B. RO C. PR D. QS

58. The accompanying diagram shows unit circle O,with radius OD = 1.

Which line segment has a length equivalent totan θ ?

A.−−−AD B.

−−−BC C.

−−−OA D.

−−−OB

59. In the accompanying diagram,−−−TS is tangent to

unit circle O at S, −−−PR ⊥ −−−OS, and−−−TS ⊥

−−−OS.

Which line segment represents sin θ?

A.−−−OR B.

−−−OS C.

−−−TS D.

−−−PR

page11 Trig Q Bank

60. Circle O has its center at the origin, OB = 1, and−−−BA ⊥

−−−OA. If m∠BOA = θ, which line segment

shown has a length equal to cos θ?

61. If sin x =√

22 and cos x =

√2

2 , the measure of anglex is

A. 45◦ B. 135◦ C. 225◦ D. 315◦

62. In the accompanying diagram of a unit circle,−−−BA

is tangent to circle O at A,−−−CD is perpendicular to

the x-axis, and−−−−OC is a radius.

Which distance represents sin θ ?

A. OD B. CD C. BA D. OB

63. If sin A = −1 and 0◦ ≤ A ≤ 360◦, find m∠A.

64. In the accompanying figure,−−−OP = 1. What are the

coordinates of point P ?

A. (sin θ, cos θ)

B. (− sin θ, − cos θ)

C. (cos θ, sin θ)

D. (− cos θ, − sin θ)

65. In the accompanying diagram, unit circle O hasradii

−−−OB,

−−−−OC, and

−−−−OD. Central angle θ is drawn

and−−−CA ⊥

−−−OB. The length of which line segment

represents sin θ ?

66. In the accompanying figure, circle O is a unitcircle. Which function is represented by the lengthof the line segment PQ ?

A. sin θ B. cos θ

C. tan θ D. cot θ

page12 Trig Q Bank

67. In the accompanying diagram of a unit circle,the ordered pair (x, y) represents the locus ofpoints forming the circle. Which ordered pair isequivalent to (x, y)?

A. (sin θ, cos θ)

B. (cot θ, tan θ)

C. (tan θ, cot θ)

D. (cos θ, sin θ)

68. In the accompanying diagram of unit circle O,−−−DB

is perpendicular to radius−−−OB, and

−−−CA ⊥

−−−OB at A.

Which line segment has a measure equivalent totangent O ?

A.−−−BD B.

−−−OA

C.−−−−OC D.

−−−CD

69. In the accompanying diagram, a unit circle isdrawn in which radius OA = 1. Angle θ is inQuadrant I,

−−−AD ⊥

−−−−OC and

−−−BC ⊥

−−−−OC. Which line

segment has a length equivalent to cos θ ?

A.−−−−OD B.

−−−−OC

C.−−−OB D.

−−−AD

70. If the terminal side of angle θ passes through thepoint (−4, 3), what is the value of cos θ ?

A. 35 B. − 3

5 C. 45 D. − 4

5

71. In a circle whose radius is 2 centimeters, a centralangle intercepts an arc of 6 centimeters. What isthe number of radians in the central angle?

72. In circle O, a central angle of 3 radians interceptsan arc of 27 meters. Find the number of metersin the length of the radius.

73. In a circle whose radius is 9 centimeters, what isthe number of radians in a central angle if thelength of the intercepted arc is 18 centimeters?

74. Circle O has a radius of 10. Find the length ofan arc subtended by a central angle measuring1.5 radians.

75. In a circle with a radius of 4 centimeters, whatis the number of radians in the central angle thatintercepts an arc of 8 centimeters?

76. An arc of a circle measures 30 centimeters and theradius measures 10 centimeters. In radians, whatis the measure of the central angle that subtendsthe arc?

77. In a circle, a central angle intercepts an arc of12 centimeters. If the radius of the circle is6 centimeters, find the number of radians in themeasure of the central angle.

page13 Trig Q Bank

78. In a circle, a central angle of 3.5 radians interceptsan arc of 24.5 centimeters. Find the number ofcentimeters in the radius of the circle.

79. Express, in terms of π, the length of the arcintercepted by a central angle of π

6 radians in acircle with radius 30.

80. In a circle whose radius is 4 centimeters, what isthe length, in centimeters, of an arc intercepted bya central angle of 2 1

2 radians?

81. In a circle whose radius is 8, the length of an arcof the circle is 2π. What is the number of radiansin the central angle subtended by the arc?

A. 16π B. π2 C. π

4 D. 4π

82. In a circle of radius 9, find the number of radiansin a central angle that intercepts an arc of 18.

83. In a circle, a central angle of 3 radians interceptsan arc of 15 centimeters. Find the length of theradius centimeters.

84. In a circle with a radius of 2.5 centimeters, acentral angle has a measure of 5 radians. What isthe length, in centimeters, of the arc interceptedby the central angle?

85. In a circle, a central angle containing 1.5 radiansintercepts an arc whose measure is 18 centimeters.The length of the radius is

A. 6 cm B. 12 cm C. 24 cm D. 27 cm

86. In a circle, a central angle of 2 radians interceptsan arc of 6 centimeters. Find the length of theradius in centimeters.

87. In a circle, a central angle of 1 12 radians intercepts

an arc with a length of 18 centimeters. Find thelength, in centimeters, of the radius of the circle.

88. In a circle of radius 8, find the length of the arcintercepted by a central angle of 1.5 radians.

89. In a circle, a central angle of 2 12 radians intercepts

an arc of length 10. What is the length of theradius of the circle?

90. In a circle, an arc of length 10 is intercepted by acentral angle of 2

3 radian. Find the radius of thecircle.

91. Express 7π18 radians in degree measure.

92. Express 5π12 radians in degrees.


94. If placed in standard position, an angle of 11π6

radians has the same terminal side as an angle of

A. −150◦ B. 150◦ C. −30◦ D. 240◦

page14 Trig Q Bank



97. In standard position, an angle of 7π3 radians has

the same terminal side as an angle of

A. 60◦ B. 120◦

C. 240◦ D. −420◦

98. Express 1.2π radians in degrees.


100. The number of degrees equal to 49π radians is

A. 60 B. 80 C. 130 D. 270


102. If placed in standard position, an angle of 116 π

radians has the same terminal side as an angle of

A. −150◦ B. −30◦ C. 150◦ D. 240◦

103. Express 3π radians in degrees.

104. Express 2π9 in degree measure.

105. Expressed in degrees, 8π3 is equivalent to

A. 240◦ B. 300◦ C. 420◦ D. 480◦


107. Express, in degree measure, an angle whose radianmeasure is 7π

3 .

108. Express in degree measure an angle of 2π5 radians.



111. Express 75◦ in radian measure.




page15 Trig Q Bank

















131. Expressed as a function of a positive acute angle,sin(−230◦) is equal to

A. sin 50◦ B. − sin 50◦

C. cos 50◦ D. − cos 50◦

132. The expression sin 240◦ is equivalent to

A. sin 60◦ B. cos 60◦

C. − sin 60◦ D. − cos 60◦

133. Expressed as a function of a positive acute angle,cot(−120)◦ is equivalent to

A. − tan 60◦ B. cot 60◦

C. − cot 30◦ D. cot 30◦

134. Which expression is equivalent to cos 120◦ ?

A. cos 60◦ B. cos 30◦

C. − sin 60◦ D. − sin 30◦

page16 Trig Q Bank

135. Which expression is not equivalent to sin 150◦?

A. sin 30◦ B. − sin 210◦

C. cos 60◦ D. − cos 60◦

136. The expression cot(−200◦) is equivalent to

A. − tan 20◦ B. tan 70◦

C. − cot 20◦ D. cot 70◦

137. Which expression is equivalent to sin 150◦?

A. cos 30◦ B. sin 30◦

C. sin(−30◦) D. − sin 30◦

138. tan(−100◦) is equivalent to

A. tan 80◦ B. tan 10◦

C. − tan 80◦ D. − tan 10◦

139. Which expression is equivalent to cos 150◦?

A. cos 60◦ B. − cos 60◦

C. cos 30◦ D. − cos 30◦

140. cos 280◦ is equivalent to

A. − sin 80◦ B. − cos 80◦

C. cos 10◦ D. cos 80◦

141. Which is equal in value to sin 180◦?

A. tan 45◦ B. cos 90◦

C. cos 0◦ D. tan 90◦

142. Which expression is equivalent to sin 200◦?

A. − sin 20◦ B. cos 20◦

C. cos 70◦ D. − sin 70◦

143. Which expression is equivalent to sin(−120◦)?

A. sin 60◦ B. − sin 60◦

C. cos 30◦ D. − sin 30◦

144. Which expression is equivalent to (n ◦ m ◦ p)(x),given m(x) = sin x, n(x) = 3x, and p(x) = x2?

A. sin (3x)2 B. 3 sin x2

C. sin2 (3x) D. 3 sin 2x

145. The expression sin (180◦ + x) is equivalent to

A. sin x B. cos x

C. − sin x D. − cos x

146. The expression cos (270◦ − A) is equivalent to

A. cosA B. − cosA

C. sinA D. − sinA

page17 Trig Q Bank

147. The expression sin(180◦ − x) is equivalent to

A. sin x B. cos x


148. The expression tan(180◦ + x) is equivalent to

A. cot x B. tan x

C. − cot x D. − tan x

149. The expression tan(180◦ − y) is equivalent to

A. −1 B.− tan y

1 + tan y

C. − tan y D.1 − tan y1 + tan y

150. The expression sin(180◦ + A) is equivalent to

A. cosA B. sinA

C. − cosA D. − sinA

151. The expression sin(90◦ − θ) is equivalent to

A. cos θ B. sin θ

C. − cos θ D. − sin θ

152. The expression cos 40◦ cos 10◦ + sin 40◦ sin 10◦ isequivalent to

A. cos 30◦ B. cos 50◦

C. sin 30◦ D. sin 50◦

153. Express sin 150◦ as a function of a positive acuteangle.

154. Express sin 150◦ as a function of a positive acuteangle.

155. Express tan 240◦ as a function of a positive acuteangle.


157. Express sin(−230◦) as a function of a positiveacute angle.

158. Express tan(−140◦) as a function of a positiveacute angle.


160. Express sin(−215◦) as a function of a positiveacute angle.


162. If sin θ = 0.3347, find the measure of positiveacute angle θ to the nearest minute.

page18 Trig Q Bank

163. Find the value of cos 42◦ 14′ to four decimalplaces.

164. Find the value of tan 27◦ 26′ to four decimalplaces.

165. If tan θ = 0.1988, find θ to the nearest minute.

166. If cosA = 0.3942, what is the value of angle A tothe nearest minute?

A. 23◦ 12′ B. 23◦ 13′

C. 66◦ 47′ D. 67◦ 48′

167. Find the value of tan 31◦ 27′ to four decimalplaces.

168. The value of cos 305◦ is

A. 0.5736 B. 0.8192

C. −0.8192 D. −0.5736

169. Find the value of cos 32◦ 32′ to four decimalplaces.

170. If sin θ = 0.5035, find the value of positive acuteangle θ to the nearest minute.

171. If sin 38◦ =x30

, what is x to the nearest integer?

172. In the right triangle ABC, m∠C = 90. IftanA = 10, what is m∠A to the nearest degree?

A. 45 B. 84 C. 85 D. 89

173. If tanA = 0.5400, find the measure of ∠A to thenearest degree.



176. If tanA = 34 , find m∠A to the nearest degree.

177. If sinA = 0.3642, find the measure of ∠A to thenearest degree.

178. If cos x = 25 what is the measure of ∠x, to the

nearest degree?

A. 23 B. 24 C. 66 D. 67

179. If tanA = 1.3000, find m∠A to the nearest degree.

180. If sin 43◦ =y20

, what is the value of y to the

nearest tenth?

page19 Trig Q Bank

181. If tanA = 12 , what is the measure of ∠A to the

nearest degree?

A. 79◦ B. 60◦ C. 30◦ D. 27◦

182. The value of sin 3π2 + cos 2π

3 is

A. 12 B. 1 1

2 C. −1 12 D. − 1

2

183. The value of sin(

3π2

)− cos

( π3

)is

A. −1 12 B. 1 1

2 C. 12 D. − 1

2

184. If θ terminates in Quadrant II and sin θ = 1213 , find

cos θ.

185. The value of cos π3 − sin 3π2 is

A. 1 12 B. 1

2 C. − 12 D. −1 1

2

186. Evaluate: cos π2 + sin 3π2

187. What is the value of cos(−120◦)?

A. 12 B. − 1

2 C.√

32 D. −

√3

2

188. Evaluate: sin 270◦ + cos 60◦

189. If sin θ = 23 and θ is in Quadrant I, what is the

value of (tan θ)(cos θ)?

A. 23 B.

√5

3 C. 3√

55 D. 2

√5

3

190. Find the numerical value of the expressionsin 30◦ + cos 60◦.

191. What is the value of cos(−240◦)?

A.√

32 B. −

√3

2 C. 12 D. − 1

2

192. What is the numerical value of the product(cos π)(sin π)?

193. What is the value of tan π3 + cos π ?

A.

√3 + 3

3B.

√3 − 3

3

C.√

3 − 1 D.√

3 + 1

194. The value of (sin 60◦)(cos 60◦) is

A. 34 B.

√2

4 C.√

33 D.

√3

4

195. If sin θ = − 45 and θ is in Quadrant IV, find tan θ.

196. What is the value of sin(−240◦)?

A. 12 B. − 1

2 C.√

32 D. −

√3

2

page20 Trig Q Bank

197. The value of sin π3 cos π is

A. −√

32 B. 1

2 C. − 12 D. 0

198. What is the numerical value of the product(tan π

4

) (cos π3

)?

199. The value of sin(−210◦) is

A.√

32 B. −

√3

2 C. 12 D. − 1

2

200. Find the value of tan(−135◦).

201. The value of sin 7π6 is

A. 12 B. − 1

2 C.√

32 D. −

√3

2

202. What is a value of arcsin(−√

22

)A. π

4 B. − π4 C. π2 D. − π2

203. The expression arccos 12 is equal to

A. 30◦ B. 45◦ C. 60◦ D. 90◦

204. The value of arcsin(−1) is

A. π B. − π2 C. π2 D. − π4

205. The value of arcsin( 12 ) + arctan(1) is

A. 120◦ B. 105◦ C. 90◦ D. 75◦

206. Find the value of arcsin(

12

)+ arccos

(√2

2

).

207. Find the value of arctan√

3.

208. The value of 2(arcsin 1) is

A. 0 B. 12 C. π D. π

2

209. Find the value of sin(arctan

√3

3

).

210. Evaluate: arcsin(cos 60◦)

211. Evaluate: csc(arcsin√

32 )

212. What is the value of sin(arccos 12 )?

A. 1 B. 12 C. 1

2

√3 D. 1

2

√2

213. The value of cos(arctan√

3 ) is

A. 1 B. 12 C. 1

2

√3 D. 1

2

√2

page21 Trig Q Bank

214. The value of tan(arcsin

√3

2

)is

A. 1 B.

√2

2C.

√3 D.

√3

2

215. The value of cos(arctan 8

15

)is

A. 817 B. − 8

17 C. 1517 D.

√16115

216. Find the value of tan(arccos

√2

2

).

217. Evaluate: cos [arcsin(−1)]

218. The value of tan(arccos

√2

2

)is

A. 1 B.√

3 C. −1 D. π4

219. What is the value of cos(arctan√

73 )?

A. 34 B. 3

16 C. 3√

77 D.

√7

4

220. What is the value of cos(arctan√

73 )?

A. 34 B. 3

16 C. 3√

77 D.

√7

4

221. If y = tan(arccos 12 ), then y equals

A. 45◦ B. 60◦ C.√

3 D.1√

3

222. What is the smallest positive value of x thatsatisfies x = arccos 1

2 ?

223. Find the value of cos(arcsin 4

5

).

224. If θ = arccos(√

32

), what is the value of sin θ ?

225. Find the value of cos(arcsin 513 ).

226. What is the value of cos(arcsin

√3

2

)?

227. What is the value of sin(arctan 1)?

A. −

√2

2B.

√2

2C.

√3

2D. −

√3

2

228. If y = sin(arccos 12 ), the value of y is

A. 12 B.

√3

2 C. 30◦ D. 60◦

229. Find tan(arcsin 513 )

page22 Trig Q Bank

230. If sin θ < 0 and tan θ = − 45 , in which quadrant

does θ terminate?

A. I B. II C. III D. IV

231. An angle that measures 5π6 radians is drawn in

standard position. In which quadrant does theterminal side of the angle lie?

232. If cos x = −√

32 , in which quadrants could ∠x

terminate?

A. I and IV, only B. II and IV, only

C. II and III, only D. I and III, only

233. If csc θ = − 43 and cos θ > 0, in which quadrant

does θ terminate?

234. If sinA < 0 and cosA < 0, in which quadrant does∠A terminate?


235. In which quadrant does θ lie if tan θ < 0 andcsc θ > 0?

236. If tanA < 0 and cosA > 0, in which quadrant does∠A terminate?


237. An angle with measure 7π4 radians is in standard

position. In which quadrant does its terminal sidelie?

238. In which quadrant do both the cosecant and secantfunctions have negative values?

239. If tanA > 0 and cosA < 0, in which quadrant does∠A terminate?


240. If sinA > 0 and cosA < 0, in which quadrant does∠A terminate?


241. If cosA = − 45 and tanA is negative, in which

quadrant does angle A terminate?


242. If csc θ = −5 and tan θ > 0, then θ must lie inQuadrant


243. If sin x = − 23 and sin x cos x > 0, in which quadrant

does angle x lie?


page23 Trig Q Bank

244. If sinA < 0 and tanA > 0, in which quadrant doesangle A terminate?


245. If tan x = − 32 and cos x > 0, then angle x terminates

in Quadrant


246. If sin θ = − 35 and cos θ < 0, then θ terminates in

Quadrant


247. If tan θ =1 +√

3

4, then angle θ may terminate in

Quadrant

A. I or III only B. II or IV only

C. III or IV only D. I, II, III, or IV

248. If sin θ = cos θ, in which quadrants may angle θterminate?

A. I, II B. II, III C. I, III D. I, IV

249. If sin x = − 23 and tan x < 0, in which quadrant does

∠x terminate?

250. Express as a single fraction the exact value ofsin 75◦.

251. If cos θ = − 45 and θ lies in Quadrant II, what is

the value of tan θ?

A. 34 B. 4

3 C. − 34 D. − 4

3

252. If θ is a positive acute angle and sin θ = a, whichexpression represents cos θ in terms of a?

A.√a B.

√1 − a2

C.1√a

D.1√

1 − a2

253. If sin θ = − 817 and tan θ is positive, what is the

value of cos θ ?

254. The expression 1 − sin2 45◦ has the same value as

A. cos 90◦ B. cos 45◦

C. sin 90◦ D. sin 22 12◦

255. If cosA = 45 and A is in Quadrant I, what is the

value of sinA · tanA ?

A. 920 B. 12

25 C. 1625 D. 16

20

256. If cos θ = − 34 and tan θ is negative, the value of

sin θ is

A. 45 B. −

√7

4 C. 74 D.

√7

4

257. If cos θ = − 12 and θ is not a third-quadrant angle,

what is sin θ ?

page24 Trig Q Bank

258. If sin θ = − 45 and tan θ is negative, what is the

value of cos θ ?

259. If sinA = k, then the value of the expression(sinA)(cosA)(tanA) is equivalent to

A. 1 B.1

kC. k D. k2

260. If x is a positive acute angle and cos x = 35 , find

the value of sin x.

261. If sin θ = 2√5

and θ is a positive acute angle, findthe value of tan θ.

262. If tan x = − 23 and angle x lies in the second

quadrant, what is the value of cos x ?

A. 3√

55 B. − 3

√5

5 C. 3√

1313 D. − 3

√13

13

263. If cos x = − 45 and tan x > 0, the value of sin x is

A. 35 B. 5

3 C. − 53 D. − 3

5

264. If cos x = 0.8, what is the value of sin x ?

A. 1.0 B. 0.2 C. 0.6 D. 0.4

265. If θ is a positive acute angle and sin 2θ =√

32 , then

(cos θ + sin θ)2 equals

A. 1 B. 1 +

√3

2

C. 30◦ D. 60◦

266. If sinA = 45 , tanB = 5

12 , and angles A and B are inQuadrant I, what is the value of sin(A + B)?

A. 6365 B. − 63

65 C. 3365 D. − 33

65

267. If sin x = 1213 , cos y = 3

5 , and x and y are acuteangles, the value of cos(x − y) is

A. 2165 B. 63

65 C. − 1465 D. − 33

65

268. If A and B are positive acute angles, sinA = 513 ,

and cosB = 45 , what is the value of sin (A + B)?

A. 5663 B. 63

65 C. 3365 D. − 16

65

269. If sin θ > 0 and sec θ < 0, in which quadrant doesthe terminal side of angle θ lie?


270. If tanA = 23 and tanB = 1

2 , what is the value oftan (A + B)?

A. 18 B. 7

8 C. 14 D. 7

4

page25 Trig Q Bank

271. If A and B are positive acute angles, sinA = 513 ,

and cosB = 45 , what is the value of sin(A + B)?

A. − 1665 B. 33

65 C. 5665 D. 63

65

272. If tanA = 8 and tanB = 12 , what is the value of

tan(A + B)?

A. 43 B. 17

10 C. − 156 D. − 17

6

273. If cos x = 1213 and sin y = 4

5 , then sin(x − y) equals

A. 7265 B. 56

65 C. − 1665 D. − 33

65

274. If ∠A and ∠B are acute angles, sinA = 45 , and

cosB = 513 , what is the value of sin(A + B)?

A. 1665 B. 46

65 C. 5665 D. 63

65

275. Since sin 75◦ = sin(30◦ + 45◦), then sin 75◦ equals

A.

√6 −√

2

4B.

−√

6 +√

2

4

C.−√

2 −√

6

4D.

√2 +√

6

4

276. If A and B are acute angles, sin A = 12 , and

sinB =√

32 , what is the value of sin(A − B)?

A. 1 B. −1 C. 12 D. − 1

2

277. If sinA = 35 , sinB = 2

3 , and ∠A and ∠B are acuteangles, what is the value of cos(A − B)?

A. −2

3B.

4√

5 − 6

15

C.4√

5 + 2

5D.

4√

5 + 6

15

278. If A and B are both acute angles, sinA = 513 and

sinB = 45 , then sin(A − B) is

A. − 3365 B. 63

65 C. 3365 D. 43

65

279. Find the value of sin( π

6 + π3

).

280. If sinA = 45 , tanB = 5

12 , and A and B are firstquadrant angles, what is the value of sin(A + B)?

A. 6365 B. − 33

65 C. 3365 D. − 63

65

281. If sinA = 35 , sinB = 5

13 , and angles A and B areacute angles, what is the value of cos(A − B)?

A. − 1265 B. 16

65 C. 3365 D. 63

65


A. cos 10◦ B. cos 150◦

C. sin 10◦ D. sin 150◦

page26 Trig Q Bank


A. cos 60◦ B. cos 80◦

C. sin 60◦ D. sin 80◦

284. The expression cos2 40 − sin2 40 has the samevalue as

A. sin 20 B. sin 80 C. cos 80 D. sin 20

285. The value of cos 16◦ cos 164◦ − sin 16◦ sin 164◦ is

A. −1 B. − 12 C. 0 D.

√3

2

286. sin 50◦ cos 30◦ + cos 50◦ sin 30◦ is equivalent to

A. cos 80◦ B. sin 20◦

C. cos 20◦ D. sin 80◦

287. Express sin 75◦ cos 15◦ − cos 75◦ sin 15◦ as a singletrigonometric function of a positive acute angle.

288. The expression 2 sin 30◦ cos 30◦ has the same valueas

A. sin 15◦ B. cos 60◦

C. sin 60◦ D. cos 15◦

289. The expression cos 80◦ cos 20◦ − sin 80◦ sin 20◦ isequivalent to

A. cos 60◦ B. cos 100◦

C. sin 100◦ D. sin 60◦

290. The expression sin 50◦ cos 40◦ + cos 50◦ sin 40◦ isequivalent to

A. sin 10◦ B. cos 10◦

C. sin 90◦ D. cos 90◦

291. Which expression is equivalent tosin 22◦ cos 18◦ + cos 22◦ sin 18◦?

A. sin 4◦ B. cos 4◦

C. sin 40◦ D. cos 40◦

292. Which expression is equivalent tocos 100◦ cos 80◦ − sin 100◦ sin 80◦?

A. 1 B. 0

C. −1 D. cos 20◦

293. Evaluate: sin 300◦ cos 90◦ + cos 300◦ sin 90◦


A. 1 B. 12 C.

√3

2 D. 0

page27 Trig Q Bank

295. The value of sin 60◦ cos 45◦ − sin 45◦ cos 60◦ is

A. 1 B. 0

C.

√6 −√

2

4D.

1

2


A. 1 B. 12 C.

√3

2 D. 0

297. What is the value ofsin 210◦ cos 30◦ − cos 210◦ sin 30◦?

A. 1 B. −1 C. 0 D. 180

298. Express in radical form:sin 90◦ cos 30◦ − cos 90◦ sin 30◦

299. sin 96◦ cos 24◦ + cos 96◦ sin 24◦ is equivalent to

A. sin 60◦ B. − sin 60◦

C. cos 60◦ D. − cos 60◦

300. cos 70◦ cos 40◦ − sin 70◦ sin 40◦ is equivalent to

A. cos 30◦ B. cos 70◦

C. cos 110◦ D. sin 70◦

301. Which expression is equivalent tosin 42◦ cos 48◦ + cos 42◦ sin 48◦?

A. 1 B. 0 C. sin 6◦ D. cos 6◦

302. The expression sin 80◦ cos 70◦ + cos 80◦ sin 70◦ isequivalent to

A. sin 10◦ B. cos 10◦

C. sin 150◦ D. cos 150◦

303. The value of sin 170◦ cos 20◦ − cos 170◦ sin 20◦ is

A. 12 B. − 1

2 C.√

32 D. −

√3

2

304. If cos 2θ = 1, a value of θ is

A. 45◦ B. 90◦ C. 180◦ D. 270◦

305. If x is a positive acute angle and sin x = 12 , what

is sin 2x?

A. −12 B. 1

2 C. −√

32 D.

√3

2

306. If θ is an acute angle such that sin θ = 513 , what is

the value of sin 2θ?

A. 1213 B. 10

26 C. 60169 D. 120

169

307. If x is an acute angle and sin x = 1213 , then cos 2x

equals

A. 25169 B. 119

169 C. − 25169 D. − 119

169

308. If sin θ =√

53 , then cos 2θ equals

A. 13 B. − 1

3 C. 19 D. − 1

9

page28 Trig Q Bank

309. If x is a positive acute angle and cos x = 19 , what

is the value of cos 12x?

A. 23 B. 1

3 C. 2√

53 D.

√5

3

310. If sin x = 23 , find the value of cos 2x in simplest

fractional form.

311. If cos θ = 18 , the positive value of sin θ

2 is

A. 32 B.

√7

4 C. 916 D. 3

4

312. If cos x = 0.8, what is a value of tan 12x ?

A. 13 B. 1

9 C. 3 D. 9

313. If sinA = 513 , find cos 2A.

314. If cos θ = − 35 , find cos 2θ and express in simplest

form.


316. If cosA = 13 , then the positive value of tan 1

2A is

A.√

2 B.√

3 C.√

33 D.

√2

2


318. If cosA = 35 and angle A is acute, find the value

of sin 12A.

319. The expression cot Θ · secΘ is equivalent to

A.cosΘ

sin2 ΘB.

sinΘ

cos2 Θ

C. cscΘ D. sinΘ

320. The expression cos (π − x) is equivalent to

A. sin x B. − sin x

C. cos x D. − cos x

321. The expressiontan θsec θ

is equivalent to

A.cos2 θsin θ

B.sin θcos2 θ

C. cos θ D. sin θ

322. The expressionsec θcsc θ

is equivalent to

A. sin θ B. cos θ C.sin θcos θ

D.cos θsin θ

323. The expression (sec2 θ)(cot2 θ)(sin θ) is equivalentto

A. sin θ B. cos θ C. csc θ D. sec θ

page29 Trig Q Bank

324. For all values of θ for which the expression is

defined,csc θsec θ

is equivalent to

A. cos θ B. sin θ C. cot θ D. tan θ


defined,sec θcsc θ

is equivalent to

A. sin θ B. cos θ C. tan θ D. cot θ

326. The expression (tan θ)(csc θ) is equivalent to

A. cos θ B. sec θ

C. csc θ D. csc θ cot θ

327. The expressionsin x • cos x

tan xis equivalent to

A. 1 B. sin2 x C. cos x D. cos2 x

328. The expressionsec θcsc θ

is equivalent to

A. cot θ B. tan θ C. cos θ D. sin θ

329. Expressed in the simplest form, csc θ · tan θ · cos θis equivalent to

A. 1 B. sin θ C. cos θ D. tan θ


is equivalent to

A. cot θ B. csc θ C. cos θ D. sin θ

331. The expressioncot θcsc θ

is equivalent to

A.cos θ

sin2 θB. sin θ C. tan θ D. cos θ

332. The expressionsec θtan θ

is equivalent to

A. sin θ B. cos θ C. sec θ D. csc θ

333. For all values of A for which the expression is

defined,cotAcscA

is equivalent to

A. cosA B. sinA C.1

cosAD.

1

sinA

334. For all values of x for which the expression isdefined, sec x · csc x · cos x is equivalent to

A. tan x B. sin x C.1

sin xD.

1

cos x


is equivalent to

A. sin θ B.sin θcos2 θ

C.cos2 θsin θ

D. cos θ

page30 Trig Q Bank


defined,cot θcsc θ

is equivalent to

A. cos θ B. sin θ C. csc θ D. tan θ

337. For all value of θ for which the expression is

defined,sec θcsc θ

is equivalent to

A. sin θ B. cos θ C. tan θ D. cot θ

338. The expression (cot θ)(sec θ) is equivalent to

A. tan θ B. cos θ C. cot θ D. csc θ

339. The expression (1 + cos x)(1 − cos x) is equivalentto

A. 1 B. sec2 x C. sin2 x D. csc2 x

340. Express (1 − cos θ)(1 + cos θ) in terms of sin θ.

341. The expression sec2 θ − tan2 θ is equal to

A. 1 B. 0

C. sin2 θ D.1

cos2 θ

342. The expression (1 − cos x)(1 + cos x) is equivalentto

A. sin x B. − sin x

C. sin2 x D. − sin2 x

343. The expression sin2 x + cos2 x − b2 is equivalent to

A. 1 B. b2

C. (1 + b)(1 − b) D. sin x cos x − b

344. The expression sin θ (cot θ − csc θ) is equivalent to

A. cos θ − sin2 θ B. 2 cos θ

C. − sin θ D. cos θ − 1

345. Expresscos 2A + sin2 A

cosAas a single trigonometric

function for all values of A for which the fractionis defined.

346. The expression cos θ(sec θ − cos θ) is equivalent to

A. 1 B. sin θ

C. sin2 θ D. − cos2 θ

347. The expressionsin2 BcosB

+ cosB is equivalent to

A. 1 B.1

cosBC.

1

secBD. sin2 B

page31 Trig Q Bank

348. The expression sec2 x + csc2 x is equivalent to

A. 1 B.1

cos x sin x

C. cos2 x sin2 x D.1

cos2 x sin2 x

349. The expressionsin2 x + cos2 x

cos xis equivalent to

A. csc x B. sec x

C. cos x · tan x D. sin x · cos x · tan x

350. Express (1 + sin θ)(1 − sin θ) in terms of cos θ.

351. The expressioncos2 x + sin2 x

sin xis equivalent to

A. sin x B. cos x C. sec x D. csc x

352. The expression sec2 θ + csc2 θ is equivalent to

A. 1 − tan2 θ B. 1 + tan2 θ

C.1

sin2 θ cos2 θD. sin2 θ cos2 θ

353. The expression1 − sin2 A2 cosA

is equivalent to

A.sinA

2B.

cosA2

C. cos 12A D. 2 cosA

354. The expressionsin2 AtanA

is equivalent to

A.sinAcosA

B. sinA cosA

C.1

sinA cosAD.

cosAsinA

355. The expression1

1 − cosA+

1

1 + cosAis equivalent

to

A.2

1 − cosAB.

2

1 − cos2 A

C.2

1 + cosAD.

2 cosA1 − cos2 A

356. The expression cos y(csc y − sec y) is equivalent to

A. cot y − 1 B. tan y − 1

C. 1 − tan y D. − cos y

357. The expressionsin2 x + cos2 x

sin xis equivalent to

A. csc x B. sec x

C. sin x cot x D. sin x cos x cot x

358. For all values of x for which the expressions aredefined, sec x − tan x is equivalent to

A. 1 B. cos x − cot x

C.1 − sin x

cos xD.

cos x − sin2 xsin x cos x

page32 Trig Q Bank

359. Express cos θ(sec θ − cos θ), in terms of sin θ.

360. Which expression always equals 1?

A. cos2 x − sin2 x B. cos2 x + sin2 x

C. cos x − sin x D. cos x + sin x

361. The expression 1 − sec x is equivalent to

A. − tan x B.cos x − 1

cos x

C.sin x − 1

sin xD.

tan xsec x − 1

362. The expressionsin 2A2 cosA

is equivalent to

A. cosA B. tanA

C. sinA D. 12 sinA

363. The expressionsin 2θ

sin2 θis equivalent to

A.2

sin θB. 2 cos θ

C. 2 cot θ D. 2 tan θ

364. The expression2 cos θsin 2θ

is equivalent to

A. csc θ B. sec θ C. cot θ D. sin θ

365. The expression2 cos xsin 2x

is equivalent to

A. cos x B. csc x C. sin x D. sec x

366. The expression sin 2A − 2 sinA is equivalent to

A. (sinA)(sinA − 2) B. (2 sinA)(sinA − 1)

C. (sinA)(2 cosA − 1) D. (2 sinA)(cosA − 1)

367. The expression cscA sin 2A is equivalent to

A. 2 sinA B. 2

C. 2 cosA D. 2 cotA

368. The expression sec x sin 2x is equivalent to

A. 12 B. 2

C. 2 cos x D. 2 sin x

369. The expressionsin 2xsin(−x)

is equivalent to

A. −2 sin x B. 2 sin x

C. −2 cos x D. 2 cos x

370. Which expression is equivalent tosin 2xcos x

?

A. 2 sin x B. tan x

C. cos 2x D. 2 cos x

page33 Trig Q Bank

371. Which trigonometric function is equivalent to the

expressionsin 2x2 sin x

?

A. tan x B. cot x C. sin x D. cos x

372. The expression1 + cos 2x

sin 2xis equivalent to

A. tan x B. cot x


373. The expression sinA cosA + sin 2A is equivalent to

A. sinA(cosA + sinA) B. cosA + 2 sinA

C. 3 sinA cosA D. cosA + 2 sin 2A

374. The expressionsin 2A

2 cos2 Ais equivalent to

A. sinA B. tanA

C. cotA D. 2 tanA

375. cos 2A + 1 is equivalent to

A. 2 cos2 A B. 2 sin2 A

C. cos2 A + 1 D. 2 sinA cosA + 1

376. The expression cos 2A − cos2 A is equivalent to

A. cos2 A + 1 B. sin2 A − 1

C. − sin2 A D. cos2 A

377. For all values of A for which the expressions are

defined,sin 2AcosA

− sinA is equivalent to

A. 1 B. cosA

C. sinA D. 2 sinA

378. The expressionsin 2A

sin2 Ais equivalent to

A. 1 B. 2

C. 2 tanA D. 2 cotA

379. The expression sin 2A + cosA is equivalent to

A. cosA(2 sinA + 1) B. cosA(cosA + 1)

C. 2(sinA + cosA) D. cosA(sinA + 1)

380. The expression cos(A − B) is equal to

A. −2 sinA sinB B. −2 cosB

C. 2 cosA cosB D. 2 sinA sinB

381. If cos 72◦ = sin x, find the number of degrees inthe measure of acute angle x.

382. In the interval 90◦ ≤ θ ≤ 180◦, find the value of θthat satisfies the equation 2 sin θ − 1 = 0.

383. Find the number of degrees in the measure of thesmallest positive angle that satisfies the equation2 cos x + 1 = 0.

page34 Trig Q Bank

384. Find the value of x in the domain 0◦ ≤ x◦ < 90◦

that satisfies the equation 2 sin x −√

2 = 0.

385. In the interval 0 ≤ x < 2π, the solutions of theequation sin2 x = sin x are

A. 0, π2 , π B. π

2 , 3π2

C. 0, π2 , 3π

2 D. π2 , π, 3π

2

386. If sin θ + cos θ = 1 and sin θ − cos θ = 1, findthe number of degrees in θ in the interval0◦ ≤ θ < 180◦.

387. Which value of A satisfies the equation2 sinA − 1 = 0?

A. 12 B. 30◦ C. 45◦ D. 60◦

388. The inequality sin θ ≥ cos θ is true for all valuesof θ in the interval

A. 0◦ ≤ θ ≤ 90◦ B. 0◦ ≤ θ ≤ 360◦

C. 45◦ ≤ θ ≤ 225◦ D. 45◦ ≤ θ ≤ 315◦

389. If cos(2x + 25)◦ = sin 35◦, find x.

390. Find a value of θ in the interval 0◦ ≤ θ < 360◦

that satisfies the equation sin2 θ − sin θ − 2 = 0.

391. Find the measure of the smallest positive anglethat satisfies the equation tan2 A − 3 = 0.

392. Which value of x does not satisfy the equationsin2 x + sin x = 0?

A. π2 B. 2π C. 3

2π D. π

393. A solution of the equation√

4 sin x + 7 = 3 is

A. π4 B. π

3 C. π6 D. π

2

394. What is the value of x in the interval 90◦≤ x≤ 180◦

that satisfies the equation sin x + sin2 x = 0?

A. 90◦ B. 135◦ C. 180◦ D. 270◦

395. In the interval 0◦ ≤ θ < 360◦, how many values ofθ satisfy the equation sin2 θ = 1

4 ?

A. 1 B. 2 C. 3 D. 4

396. Which is a value of x if sin 60◦ = cos(x + 10◦)?

A. 10◦ B. 20◦ C. 50◦ D. 60◦

397. Find the value of x between 0◦ and 360◦ whichsatisfies the equation sin2 x + 3 sin x + 2 = 0.

398. If cos(x + 30◦) = sin x, a measure of angle x is

A. 15◦ B. 30◦ C. 45◦ D. 60◦

page35 Trig Q Bank

399. In the interval 0◦ ≤ x < 360◦, sin x = cos x when xis

A. 45◦ only B. 45◦ and 225◦ only

C. 135◦ and 315◦ only D. 225◦ only

400. Which value of x satisfies the equationsin 40◦ = cos x ?

A. 20◦ B. 40◦ C. 50◦ D. 80◦

401. What is a positive value of tan 12x, when

sin x = 0.8?

A. 0.5 B. 0.4 C. 0.33 D. 0.25

402. What value of x in the interval 0◦ ≤ x ≤ 180◦

satisfies the equation√

3 tan x + 1 = 0?

A. −30◦ B. 30◦ C. 60◦ D. 150◦

403. Find a value for θ in the interval 90◦ ≤ θ ≤ 270◦

that satisfies the equation 2 sin θ + 1 = 0.

404. If 3x is the measure of a positive acute angle andcos 3x = sin 60◦, find the value of x.

405. Find a positive acute angle θ such that4 cot θ sin θ = 2.

406. If sin (2x + 20)◦ = cos 40◦, find x.

407. Which two values of x satisfy the equation√3 − 2 cos x = 2 ?

A. 150◦ and 210◦ B. 120◦ and 240◦

C. 60◦ and 300◦ D. 30◦ and 330◦

408. What is one possible value of θ in the equationcot θ = cos θ?

A. 0◦ B. 45◦ C. 90◦ D. 180◦

409. In the interval 90◦ < x < 270◦, what is the solutionto csc x = −2?

A. 120◦ B. 150◦ C. 210◦ D. 240◦

410. If θ is a positive acute angle and 2 cos θ + 3 = 4,find the number of degrees in θ.

411. Which value of θ satisfies the equation2 cos2 θ − cos θ = 0?

A. π3 B. π

4 C. π6 D. 0

412. Solve for the smallest non-negative value of θ:√

3 cos θ + 1 = 2

413. What is the number of degrees in the value of θthat satisfies the equation 2 cos θ − 1 = 0 in theinterval 180◦ ≤ θ ≤ 360◦?

414. If cos (2x − 25)◦ = sin 55◦, find the value of x.

page36 Trig Q Bank

415. If θ is an angle in Quadrant I and tan2θ − 4 = 0,what is the value of θ to the nearest degree ?

A. 1 B. 2 C. 63 D. 75

416. In the interval 0 ≤ θ < 2π, the number of solutionsof the equation sin θ = cos θ is

A. 1 B. 2 C. 3 D. 4

417. Find m∠θ in the interval 180◦ ≤ θ ≤ 270◦ thatsatisfies the equation 2 cos θ + 1 = 0.

418. If cos(2x− 1)◦ = sin(3x+6)◦, then the value of x is

A. −7 B. 17 C. 35 D. 71

419. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation3 cos 2x + cos x + 2 = 0.

420. If sin 2A = cos 3A, then m∠A is

A. 1 12 B. 5 C. 18 D. 36

421. Find, to the nearest degree, all values of xbetween 0◦ and 360◦ that satisfy the equation2 sin x + 4 cos 2x = 3. [Show or explain theprocedure used to obtain your answer.]

422. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation6 cos2 x + 2 = 0. [Show or explain the procedureused to obtain your answer.]

423. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation3+ tan2 x = 5 tan x. [Show or explain the procedureused to obtain your answer.]

424. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation3 cos 2x + sin x − 1 = 0. [Show or explain theprocedure used to obtain your answer.]

425. Which value of x satisfies the equationsin(3x + 5)◦ = cos(4x + 1)◦?

A. 30 B. 24 C. 12 D. 4

426. If cot (x − 10)◦ = tan (4x)◦, a value of x is

A. 10 B. 20 C. 30 D. 40

427. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation2 tan2 x − 5 tan x − 1 = 0. [Show or explain theprocedure used to obtain your answer.]

428. If cos x◦ = sin(2x − 30)◦, a value of x can be

A. 20 B. 40 C. 50 D. 60

page37 Trig Q Bank

429. Find, to the nearest ten minutes, all values of x inthe interval 0◦ ≤ x < 360◦ that satisfy the equationcos 2x − sin2 x + sin x + 1 = 0. [Show or explainthe procedure used to obtain your answer.]

430. What is the positive value of sin x that satisfiesthe equation sin2 x + 4 sin x − 5 = 0?

431. Find, to the nearest degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation3 cos 2x + 5 sin x − 2 = 0. [Show or explain theprocedure used to obtain your answer.]

432. If cos(2x + 10)◦ = sin(x + 20)◦, a value of x is

A. 20 B. 30 C. 40 D. 60

433. What is the total number of solutions for theequation 3 tan2 A + tanA − 2 = 0 in the interval0 ≤ A ≤ π ?

A. 1 B. 2 C. 3 D. 4

434. Find, to the nearest degree, all values of θ in theinterval 0◦ ≤ θ < 360◦ that satisfy the equation3 cos 2θ − sin θ − 2 = 0. [Show or explain theprocedure used to obtain your answer.]

435. If tan x = cot(2x − 6), then m∠x is

A. 28 B. 32 C. 45 D. 84

436. Find the value of acute angle A ifsinA

cos 50◦= 1.

437. In the interval 0◦ ≤ x ≤ 360◦, what is the totalnumber of values of x that satisfy the equationsin2 x + sin x − 1 = 0?

438. Find, to the nearest ten minutes or nearesttenth of a degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation4 cos 2x − 2 cos x + 3 = 0.

439. Find, to the nearest tenth of a degree, all valuesof θ in the interval 0◦ ≤ θ < 360◦ that satisfy theequation 5 sin2 θ − 9 cos θ − 3 = 0.

440. Find, to the nearest ten minutes or the nearesttenth of a degree, all values of θ in theinterval 0◦ ≤ θ < 360◦ that satisfy the equation4 cos2 θ = 3 + 3 sin θ.

441. Find, to the nearest ten minutes or nearesttenth of a degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation6 cos2 x − 5 sin x − 5 = 0.

442. Find, to the nearest ten minutes or nearesttenth of a degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation6 sin x + 3 = 2 csc x.

443. If tan(x + 20) = cot x, a value of x is

A. 35 B. 45 C. 55 D. 70

444. Find all values of θ in the interval 0 ≤ θ < 360◦

that satisfy the equation sin θ = 2 + 3 cos 2θ.Express your answer to the nearest ten minutes ornearest tenth of a degree.

page38 Trig Q Bank

445. Find, to the nearest ten minutes or nearesttenth of a degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation4 sin2 x − 5 sin x − 6 = 0.

446. Find all values of x in the interval 0 ≤ x < 360◦

that satisfy the equation 4 cos2 x − 5 sin x − 5 = 0.Express your answer to the nearest ten minutes ornearest tenth of a degree.

447. A solution of the equation cos 2θ + sin 2θ = −1 is

A. 240◦ B. 135◦ C. 45◦ D. −30◦

448. Find, to the nearest degree, all positive valuesof θ less than 360◦ that satisfy the equation2 tan2 θ − 2 tan θ = 3.

449. What is one solution of the equation(sin x + cos x)2 = 2?

A. π4 B. π

3 C. π2 D. 0

450. Which value of θ satisfied the equation2 sin2 θ − 5 sin θ − 3 = 0?

A. 300◦ B. 210◦ C. 150◦ D. 30◦

451. Find to the nearest degree, all values of θ in theinterval 0◦ ≤ θ < 360◦ that satisfy the equation2 sin2 θ + 2 cos θ − 1 = 0.

452. Find all values of x in the interval 0◦ ≤ x ≤ 360◦

that satisfy the equation 3 cos 2x + 2 sin x = −1.Express your answer to the nearest ten minutes ornearest tenth degree.

453. Find, to the nearest ten minutes or nearesttenth of a degree, all values of θ in theinterval 0◦ ≤ θ ≤ 360◦ that satisfy the equation5 sin2 θ − 7 cos θ + 1 = 0.

454. If sin(x − 3)◦ = cos(2x + 6)◦, then the value of x is

A. −9 B. 26 C. 29 D. 64

455. Find all positive values of θ less than 360◦ thatsatisfy the equation 2 cos 2θ − 3 sin θ = 1. Expressyour answers to the nearest ten minutes or nearesttenth of a degree.

456. Find, to the nearest ten minutes or nearesttenth of a degree, all values of x in theinterval 0◦ ≤ x < 360◦ that satisfy the equation2 sin 2x + cos x = 0.

457. If sin(x + 20◦) = cos x, the value of x is

A. 35◦ B. 45◦ C. 55◦ D. 70◦

458. Given angle A in Quadrant I with sinA =12

13and

angle B in Quadrant II with cosB = −3

5, what is

the value of cos (A − B)?

A.33

65B. −

33

65C.

63

65D. −

63

65

page39 Trig Q Bank

459. Solve the equation 2 tanC − 3 = 3 tanC − 4algebraically for all values of C in the interval0◦ ≤ C < 360◦.

460. Find all values of θ in the interval 0◦≤ θ < 360◦

that satisfy the equation sin 2θ = sin θ.

461. Solve algebraically for all values of θ in theinterval 0◦ ≤ x ≤ 360◦.

2 sin2 θ − 4 sin θ = cos2 θ − 2

Express your answers to the nearest degree.

462. Solve the equation cos Θ = 2 + 3 cos 2Θ for allvalues of Θ, to the nearest tenth of a degree, inthe interval 0◦ ≤ Θ < 360◦.

463. Find all values of θ in the interval 0◦ ≤ θ < 360◦

that satisfy the equation 3 cos 2θ + 2 sin θ + 1 = 0,and round all answers to the nearest hundredth ofa degree. [Only an algebraic solution can receivefull credit.]

464. Find all values of x in the interval 0◦ ≤ x < 360◦

that satisfy the equation 3 cos x + sin 2x = 0.

465. Find, to the nearest degree, all values of θ in theinterval 0◦ ≤ θ ≤ 180◦ that satisfy the equation8 cos2 θ − 2 cos θ − 1 = 0.

466. Find, to the nearest degree, all values of θ in theinterval 0◦ ≤ θ < 360◦ that satisfy the equation3 cos 2θ + sin θ − 1 = 0.

467. Solve algebraically for all values of θ in theinterval 0◦ ≤ θ < 360◦ that satisfy the equation

sin2 θ1 + cos θ

= 1.

468. Navigators aboard ships and airplanes use nauticalmiles to measure distance. The length of anautical mile varies with latitude. The length of anautical mile, L, in feet, on the latitude line θ isgiven by the formula L = 6,077 − 31 cos 2θ.

Find, to the nearest degree, the angleθ, 0◦ ≤ θ ≤ 90◦, at which the length of a nauticalmile is approximately 6,076 feet.

469. On a monitor, the graphs of two impulses arerecorded on the same screen, where 0◦ ≤ x < 360◦.The impulses are given by the following equations:

y = 2 sin2 x

y = 1 − sin x

Find all values of x, in degrees, for which the twoimpulses meet in the interval 0◦ ≤ x < 360◦. [Onlyan algebraic solution will be accepted.]

470. In the interval 0◦ ≤ A < 360◦, solve for all valuesof A in the equation cos 2A = −3 sinA − 1.


that satisfy the equation 5 sin θ + 2 cos 2θ − 3 = 0.Express your answer to the nearest ten minutes ornearest tenth of a degree.


that satisfy the equation 3 cos 2θ = 7 cos θ. Expressyour answer to the nearest tenth of a degree ornearest ten minutes.

page40 Trig Q Bank

473. In ÂBC, a = 15, c = 10, and sinA = 0.45. FindsinC.

474. In ÂBC, b = 6, c = 3, and sinB = 0.4. Find thevalue of sinC.

475. If a = 4, b = 6, and sinA = 35 in ÂBC, then sinB

equals

A. 320 B. 6

10 C. 810 D. 9

10

476. In ÂBC, a = 10, b = 8, and sinB = 34 . Find sinA.

477. In acute triangle ABC, a= 3, b= 4, and sinA= 0.3.What is the value of sinB ?

478. In ÂBC, a = 10, b = 6, and sinB = 25 . Express

sinA in simplest fractional form.

479. In ÂBC, sinC = 14 , c = 6, and a = 12. Find

sinA.

480. In ÂBC, a = 6, b = 8, and sinA = 14 . What is

the value of sinB ?

481. In ÂBC, a = 5, sinA = 15 , and b = 4. Find sinB.

482. In ÂBC, a = 5, b = 7, and sinA = 37 . What is

sinB ?

483. In ÂBC, a = 5, b = 6, and sinB = 35 . Find the

number of degrees in acute angle A.

484. In ÂBC, sinA = 0.25, a = 5, and b = 10. Findthe value of sinB.

485. In ÂBC, b = 12, c = 8, and sinB = 12 . Find the

value of sinC.

486. In ÂBC, a = 6, b = 9, and sinA = 23 . Find sinB.

487. In ÂBC, side a = 3, side c = 3√

2, andm∠A = 45. Find m∠C.

488. In acute triangle ABC, side a = 10, side b = 12,and m∠A = 42. Find m∠B to the nearest degree.

489. In ÂBC, m∠A = 33, a = 12, and b = 15. FindsinB to the nearest thousandth.

490. In ÂBC, a = 10, b = 16, and m∠A = 30. FindsinB.

491. In ÂBC, m∠A = 30, a = 8, and b = 12. FindsinB.

492. In ÂBC, m∠A = 38, a = 11, b = 15, and ∠B isan obtuse angle. Find the measure of ∠C to thenearest degree. [Show or explain the procedureused to obtain your answer.]

page41 Trig Q Bank

493. In ÂBC, m∠A = 30, b = 14, and a = 10. FindsinB.

494. In ÂBC, c = 20, a = 10, and m∠A = 30. Findm∠C.

495. In triangle ABC, if m∠A = 30, a = 6, and b = 8,then sinB is

A. 23 B. 3

4 C. 610 D. 8

10

496. In ÂBC, side a = 18, sinA = 34 , and sinB = 2

3 .Find the length of side b.

497. In ^RST , sin T = 15 , m∠R = 30, and r = 15. What

is the length of t?

498. In ÂBC, a = 24, sin A = 34 , and sin B = 1

2 .Find b.

499. In ÂBC, sinA = 14 , sinB = 1

8 , and b = 20. Whatis the length of a?

500. In ÂBC, sinA = 0.3, sinB = 0.8, and b = 12.Find the length of side a.

501. In ÂBC, a = 2, sinA = 23 , and sinB = 5

6 . Findthe length of side b.

502. In ÂBC, sinA = 13 , m∠B = 30, and a = 12.

What is the length of b?

503. In ÂBC, sinA = 12 , b = 20, and m∠B = 45.

What is the length of side a?

A. 10√

33 B. 10 C. 10

√2 D. 20

√2

504. In ÂBC, a = 12, sinA = 0.45, and sinB = 0.15.Find b.

505. In ÂBC, sinA = 23 , sinB = 4

5 , and side a = 20.Find side b.

506. In ÂBC, a = 10, sinA = 0.30, and sinC = 0.24.Find c.

507. In ÂBC, sinA = 0.4293, sinC = 0.4827, anda = 34.5 centimeters. Find, to the nearest tenth ofa centimeter, the measure of c.

508. In ÂBC, sin A = 45 , sinC = 2

3 , and a = 18.Find c.

509. In ÂBC, m∠A = 30◦, sinB = 34 , and a = 8. Find

the value of b.

510. In ÂBC, a = 5, sinA = 0.35, and sinB = 0.21.Find the measure of side b.

page42 Trig Q Bank

511. In ÂBC, if sinA = 45 , sinB = 3

8 , and a = 24,find b.

512. In ÂBC, sinA = 12 , sinC = 1

3 , and a = 12. Findthe length of side c.

513. In right triangle ABC, m∠C = 90, a = 4, andsinA = 1

2 . What is the length of the hypotenuse?

A. 4√

3 B.8√

3

3C. 8 D. 8

√2

514. In triangle ABC, sinA = 0.3, sinB = 0.4, anda = 12. Find b.

515. In triangle ABC, sinA = 0.3, sinB = 0.4, anda = 6. Find b.

516. In ÂBC, m∠A = 35, m∠B = 82, and side a = 4inches. Find the length of side b to the nearesttenth of an inch.

517. In ÂBC, m∠A = 30, m∠B = 65, and BC = 10.Find AC to the nearest tenth.

518. In ÂBC, m∠A = 35, m∠C = 60, andAC = 12 meters. Find the length of

−−−BC to the

nearest meter.

519. In ^FUN, f = 4, m∠F = 26, and m∠N = 67.Find the value of n to the nearest integer.

520. In ÂBC, m∠A = 45, m∠B = 30, and side a = 10.What is the length of side b ?

A. 5√

2 B. 5√

3 C. 10√

2 D. 10√

3

521. In ÂBC, m∠A = 75, m∠B = 40, and b = 35.What is the measure of side c ?

A.35 sin 40◦

sin 65◦B.

35 sin 75◦

sin 40◦

C.35 sin 40◦

sin 75◦D.

35 sin 65◦

sin 40◦

522. In ÂBC, m∠A = 40, m∠B = 70, and AC = 5centimeters. Find the length of

−−−AB in centimeters.

523. In isosceles triangle ABC, AC = BC = 20,m∠A = 68, and

−−−CD is the altitude to side

−−−AB.

What is the length of−−−CD to the nearest tenth?

A. 49.5 B. 18.5 C. 10.6 D. 7.5

524. If a = 5, c = 4, and m∠A = 40, then which typeof triangle, if any, can be constructed?

A. a right triangle, only

B. an acute triangle, only

C. an obtuse triangle, only

D. no triangle

page43 Trig Q Bank

525. If m∠A = 32, a = 5, and b = 3, it is possible toconstruct

A. an obtuse triangle

B. two distinct triangles

C. no triangles

D. a right triangle

526. Determine the maximum number of trianglespossible when m∠A = 150, a = 14, and b = 10.

527. How many distinct triangles can be formed ifa = 20, b = 30, and m∠A = 30?

A. 1 B. 2 C. 3 D. 0

528. If a = 5, c = 18, and m∠A = 30, what is thetotal number of distinct triangles that can beconstructed?

A. 1 B. 2 C. 3 D. 0

529. If m∠A = 45, AB = 10, and BC = 8, the greatestnumber of distinct triangles that can be constructedis

A. 1 B. 2 C. 3 D. 0

530. If m∠A = 125, AB = 10, and BC = 12, whatis the number of distinct triangles that can beconstructed?

A. 1 B. 2 C. 3 D. 0

531. If a = 5√

2, b = 8, and m∠A = 45, how manydistinct triangles can be constructed?

A. 1 B. 2 C. 3 D. 0

532. If a = 5, b = 7, and m∠A = 30, how many distincttriangles can be constructed?

A. 1 B. 2 C. 3 D. 0

533. In ÂBC, m∠A = 30, a = 4, and b = 6. Whichtype of angle is ∠B ?

A. either acute or obtuse

B. obtuse, only

C. acute, only

D. right

534. How many distinct triangles may be constructed ifa = 4, b = 5, and m∠A = 30?

535. If m∠A = 35, a = 7, and b = 10, how many distincttriangles can be formed?

A. 1 B. 2 C. 3 D. 0

536. If m∠A = 48, a = 7, and b = 9, the number ofdistinct triangles that can be constructed is

A. 1 B. 2 C. 3 D. 0

page44 Trig Q Bank

537. If m∠A = 30, a = 11, and b = 12, the number ofdistinct triangles that can be constructed is

A. 1 B. 2 C. 3 D. 0

538. How many distinct triangles can be constructed ifm∠A = 30, b = 12, and a = 7?

A. 1 B. 2 C. 3 D. 0

539. How many distinct triangles can be formed ifm∠A = 30, b = 12, and a = 6?

A. 1 B. 2 C. 3 D. 0

540. If m∠A = 30, a =√

5, and b = 6, the number oftriangles that can be constructed is

A. 1 B. 2

C. 0 D. an infinite number

541. If m∠A = 45, b = 6√

2, and a = 6, then ÂBC

A. is not unique

B. is a right triangle

C. is an obtuse triangle

D. cannot by constructed

542. If m∠A = 40, a = 6, and b = 8, how many distincttriangles can be constructed?

543. If a = 6, b = 5, and m∠A = 30, the number ofdistinct triangles which can be constructed is

A. 1 B. 2 C. 3 D. 0

544. If the measure of ∠A = 40◦, a = 5, and b = 6,how many different triangles can be constructed?

A. 1 B. 2 C. 3 D. 0

545. If m∠A = 35, b = 3, and a = 4, how many differenttriangles can be constructed?

A. No triangles can be constructed.

B. two triangles

C. one right triangle, only

D. one obtuse triangle, only

546. Sam needs to cut a triangle out of a sheet of paper.The only requirements that Sam must follow arethat one of the angles must be 60◦, the sideopposite the 60◦ angle must be 40 centimeters,and one of the other sides must be 15 centimeters.How many different triangles can Sam make?

A. 1 B. 2 C. 3 D. 0

547. What is the total number of distinct trianglesthat can be constructed if AC = 13, BC = 8, andm∠A = 36?

A. 1 B. 2 C. 3 D. 0

page45 Trig Q Bank

548. How many distinct triangles can be formed ifm∠A = 30, side b = 12, and side a = 8?

A. 1 B. 2 C. 3 D. 0

549. Sam is designing a triangular piece for a metalsculpture. He tells Martha that two of the sidesof the piece are 40 inches and 15 inches, and theangle opposite the 40-inch side measures 120◦.Martha decides to sketch the piece that Samdescribed. How many different triangles can shesketch that match Sam’s description?

A. 1 B. 2 C. 3 D. 0

550. A landscape designer is designing a triangulargarden with two sides that are 4 feet and 6 feet,respectively. The angle opposite the 4-foot side is30◦. How many distinct triangular gardens can thedesigner make using these measurements?

551. An architect commissions a contractor to producea triangular window. The architect describes thewindow as ÂBC, where m∠A = 50, BC = 10inches, and AB = 12 inches. How many distincttriangles can the contractor construct using thesedimensions?

A. 1 B. 2

C. more than 2 D. 0

552. A box contains one 2-inch rod, one 3-inch rod,one 4-inch rod, and one 5-inch rod. What is themaximum number of different triangles that can bemade using these rods as sides?

A. 1 B. 2 C. 3 D. 4

553. If m∠A = 68, side a = 10, and side b = 24, howmany distinct triangles can be constructed?

A. 1 B. 2 C. 3 D. 0

554. If side a = 16, side b = 20, and m∠A = 30, howmany distinct triangles can be constructed?

A. one acute triangle, only

B. two triangles

C. one obtuse triangle, only

D. no triangles

555. If m∠A = 50, side a = 6, and side b = 10, what isthe maximum number of distinct triangles that canbe constructed?

A. 1 B. 2 C. 3 D. 0

556. How many distinct triangles can be constructed ifm∠A = 60, side a = 5

√3, and side b = 10?

A. 1 B. 2 C. 3 D. 0

557. In ÂBC, m∠A = 30, a = 12, and b = 10. Whichtype of triangle is ÂBC?

A. acute B. isosceles

C. obtuse D. right

page46 Trig Q Bank

558. If m∠A = 28◦, a = 20, and b = 25, what is themaximum number of distinct triangles that can beconstructed?

A. 1 B. 2 C. 3 D. 0

559. If m∠ABC = 135, AC = 9, and AB = 10, what isthe maximum number of distinct triangles that canbe constructed?

A. 1 B. 2 C. 3 D. 0

560. What is the maximum number of distinct trianglesthat can be formed if m∠A = 30, b = 8, and a = 5?

A. 1 B. 2 C. 3 D. 0

561. In ÂBC, cosC = −0.2, a = 8, and b = 10. Findthe length of side c.

562. In ÂBC, a = 2, c = 6, and cosB = 16 . Find b.

563. In ÂBC, a = 4, b = 3, and cosC = − 12 . What is

the length of c ?

A. 7 B.√

13 C.√

37 D.√

19

564. In ÂBC, a = 8, b = 9, and cosC = 23 . Find c.

565. In ^CAT , a = 4, c = 5, and cos T = 18 . What is

the length of t ?

566. In ^DEF, if side d = 14, side e = 10, and sidef = 12, find m∠F to the nearest degree.

567. To the nearest degree, what is the measure of thelargest angle in a triangle with sides measuring 10,12, and 18 centimeters?

A. 109 B. 81 C. 71 D. 32

568. In ÂBC, a = 6, b = 7, and c = 8. What is cosAin simplest fractional form?

A. 316 B. 11

16 C. 7796 D. 51

112

569. In ÂBC, a = 8, b = 2, and c = 7. What is thevalue of cosC ?

A. − 1932 B. − 11

28 C. 109112 D. 19

32

570. In a triangle, the sides measure 3, 5, and 7. Whatis the measure, in degrees, of the largest angle?

A. 60 B. 90 C. 120 D. 150

571. In ÂBC, a = 6, b = 7, and m∠B = 30. FindsinA.

572. In ÂBC, a = 6, b = 4, and c = 9. The value ofcosC is

A. 6172 B. − 29

48 C. 23 D. 4

9

page47 Trig Q Bank

573. In ÂBC, a = 8, b = 5, and c = 9. What is thevalue of cosA ?

A. − 14 B. 1

4 C. − 715 D. 7

15

574. The sides of a triangle measure 6, 7, and 9. Whatis the cosine of the largest angle?

A. − 484 B. 81 C. 4

84 D. − 181

575. In ÂBC if a = 8, b = 5, and c = 9, then cosA is

A. 715 B. − 7

15 C. 14 D. − 1

4

576. In ÂBC, a = 5, b = 6, and c = 8. Find cosA.

577. In ÂBC, a = 1, b = 1, and c =√

2. What is thevalue of cosC ?

A. 1 B.√

2 C. 12

√2 D. 0

578. In ÂBC, a = 6, b = 5, and c = 8. CosA equals

A. 7580 B. 53

80 C. − 380 D. 53

60

579. In ÂBC, a = 4, b = 3 and c = 3. What is thevalue of cosA ?

A. 118 B. − 1

18 C. 19 D. − 1

9

580. In ÂBC, a = 5, b = 4, and c = 2. What is thevalue of cosA ?

A. 516 B. − 5

16 C. 254 D. − 25

4

581. In ÂBC, a = 7, b = 5, and c = 8. What is thevalue of cosC ?

A. 0 B. − 17 C. 2

5 D. 17

582. In ÂBC, if a = 5, b = 6, and m∠C = 60, thevalue of c is

A. 1 B.√

31 C.√

41 D.√

51

583. In triangle ABC, a = 2, b = 3, and c = 4. What isthe value of cosC ?

A. − 14 B. 7

8 C. − 12 D. 16

584. In triangle ABC, a = 5, b = 7, and c = 8. Themeasure of ∠B is

A. 30◦ B. 60◦ C. 120◦ D. 150◦

585. In ÂBC, if a = 4, b = 3, and c = 3, then thevalue of cosA is

A. 23 B. 1

9 C. − 19 D. − 2

3

586. In ÂBC, a = 6, b = 10, and m∠C = 120. Whatis the length of c?

page48 Trig Q Bank

587. In ÂBC, a = 1, b = 1, and m∠C = 120. Thevalue of c is

A. 1 B.√

2 C.√

2.5 D.√

3

588. In ^DEF if d =√

3, e = 4, and m∠F = 30, thelength of f is

A. 7 B.√

17 C.√

7 D.√

3

589. In ÂBC, a = 3, b = 8, and m∠C = 60. Find thelength of side c.

590. In triangle ABC, a = 5, b = 8, and m∠C = 60.Find the length of side c.

591. In ÂBC, a = 3, b = 5, and m∠C = 120◦. Findthe value of c.

592. In ÂBC, a = 6, b = 12, and m∠C = 60. What isthe length of side c to the nearest integer?

A. 5 B. 10 C. 11 D. 20

593. In ÂBC, AC = 18, BC = 10, and cosC = 12 .

Find the area of ÂBC to the nearest tenth of asquare unit.

594. In ÂBC, m∠B = 30 and side a = 6. If the areaof the triangle is 12, what is the length of side c?

595. In ÂBC, m∠C = 30 and a = 8. If the area ofthe triangle is 12, what is the length of side b?

A. 6 B. 8 C. 3 D. 4

596. In ÂBC, m∠C = 30 and a = 24. If the area ofthe triangle is 42, what is the length of side b?

597. The area of ÂBC is 20. If a = 10 and b = 8,find the number of degrees in the measure ofacute angle C.

598. In ÂBC, a = 8 and b = 8. If the area of ÂBCis 16, find m∠C.

599. The area of ÂBC is 100 square centimeters. Ifc = 20 centimeters and m∠A = 30, then b is equalto

A. 20 cm B. 500 cm

C. 20√

3 cm D. 10√

2 cm

600. In ÂBC, a = 8, b = 9, and m∠C = 135. What isthe area of ÂBC?

A. 18 B. 36 C. 18√

2 D. 36√

2

601. In ÂBC, side a is twice as long as side b andm∠C = 30. In terms of b, the area of ÂBC is

A. 0.25b2 B. 0.5b2

C. 0.866b2 D. b2

page49 Trig Q Bank

602. If m∠B = 60, a = 6, and c = 10, what is the areaof ÂBC ?

A. 15 B. 30 C. 15√

3 D. 30√

3

603. In ÂBC, a = 8, b = 7, and m∠C = 30. What isthe area of ÂBC ?

604. If a = 14, e = 16, and m∠C = 30, find the area ofÂCE.

605. In ÂBC, m∠A = 60, b = 4, and c = 4. What isthe area of ÂBC ?

606. In ^NEW, m∠N = 60, NE = 8, and NW = 6.Find the area of ^NEW.

607. In ^RST , r = 8, s = 10, and m∠T = 120. Expressthe area of ^RST in radical form.

608. In ÂBC, a = 16, b = 30, and m∠C = 150. Findthe area of ÂBC.

609. Find the area of ÂBC if a = 8, b = 10, andm∠C = 30.

610. In ÂBC, b = 3, c = 4, and ∠A = 45◦. Expressedin simplest radical form, what is the area ofÂBC ?

611. In ÂBC, AB = 8, AC = 6, and m∠CAB = 150.Find the area of the triangle.

612. What is the area of ÂBC if a = 8, b = 6, andsinC = 0.75?

A. 9 B. 18 C. 36 D. 72

613. Find the area of ÂBC is a = 6, b = 12, andm∠C = 150.

614. Find, to the nearest tenth, the area of ÂBC ifa = 6, b = 10, and m∠C = 18.

615. In ÂBC, a = 6, b = 8, and sinC = 14 . Find the

area of ÂBC.

616. Find the area of ÂBC if m∠A = 30, b = 10, andc = 5.

617. In ^PQR, PQ = 5 cm, QR = 6 cm, and m∠Q = 30.Find the area of ^PQR in square centimeters.

618. Two sides of a triangle measure 6 and 8, and themeasure of the included angle is 150◦. The areaof the triangle is

A. 24√

3 B. 24 C. 12√

3 D. 12

619. In ÂBC, a = 12, b = 8, and m∠C = 30. Findthe area of ÂBC.

620. In ÂBC, sinA : sinB : sinC = 4 : 5 : 6. Find thevalue of c when a = 10.

page50 Trig Q Bank

621. In ÂBC, sinA = 12 and sinB = 1

2

√2. The value

of ba is

A. 12 B. 2 C.

√2 D. 1

2

√2

622. In ÂBC, the lengths of sides a, b, and c are inthe ratio 4 : 6 : 8. Find the ratio of the cosine of∠C to the cosine of ∠A. [Show or explain theprocedure used to obtain your answer.]

623. The building lot shown in the accompanyingdiagram is shaped like an isosceles triangle withAB = AC and m∠BAC = 53◦ 10′. The area ofthe lot is one acre. Find the lengths of each ofthe three sides to the nearest foot. [One acre =43,560 ft2] [Show or explain the procedure used toobtain your answer.]

624. In parallelogram ABCD, AD = 10, AB = 12, anddiagonal BD = 18. Find the measure of angle A tothe nearest ten minutes.

625. A frame is constructed in the form of an isoscelestrapezoid. Each base angle measures 72◦ 20′, thelonger base is 12.0 feet, and each nonparallel sidemeasures 5.0 feet. Find, to the nearest tenth, thenumber of feet in a diagonal brace of this frame.[Show or explain the procedure used to obtainyour answer.]

626. The distance from A to C is 40 miles andthe distance from C to B is 70 miles. Ifm∠ACB = 110, find AB to the nearest mile. [Showor explain the procedure used to obtain youranswer.]

627. In the accompanying diagram of ÂBC,AC = 30 centimeters, m∠B = 100, and m∠A = 50.Find the area of ÂBC to the nearest squarecentimeter. [Show or explain the procedure usedto obtain your answer.]

628. The beam of a searchlight situated at an offshorepoint W sweeps back and forth between shorepoints A and B. Point W is located 12 kilometersfrom A and 25 kilometers from B. The distancebetween A and B is 29 kilometers. Find themeasure of ∠AWB to the nearest ten minutes.[Show or explain the procedure used to obtainyour answer.]

629. The angle of elevation from a ship at point A tothe top of a lighthouse, point B, is 43◦. Whenthe ship reaches point C, 300 meters closer to thelighthouse, the angle of elevation is 56◦. Find tothe nearest meter, the height to the lighthouse, BD.[Show or explain the procedure used to obtainyour answer.]

page51 Trig Q Bank

630. As shown in the accompanying diagram, a kite isflying at the end of a 25-meter string. If the stringmakes an angle of 65◦ with the ground, how high,to the nearest meter, is the kite?

631. In the accompanying diagram of trapezoid ABCD,−−−AB ⊥

−−−BC,

−−−BA ⊥

−−−AD, and

−−−AC ⊥

−−−CD. If AC = 15,

and m∠D = 31, find the area of trapezoid ABCDto the nearest integer.

632. In the accompanying diagram, ABCD is a trapezoidwith altitudes

−−−−DW and

−−−CZ drawn, CD = 17.3,

DA = 8.6, m∠A = 68◦, and m∠B = 53◦. Find, tothe nearest tenth, the perimeter of ABCD.

633. In the accompanying diagram, altitude−−−EH is

drawn in trapezoid DEFG, DE = 10, EF = 9,FG = 8, and GD = 15. What is m∠D to thenearest degree?

A. 37 B. 53

C. 60 D. 80

634. A 100-foot wire is extended from the ground tothe top of a 60-foot pole, which is perpendicularto the level ground. To the nearest degree, whatis the measure of the angle that the wire makeswith the ground?

A. 31 B. 37 C. 53 D. 59

635. In the accompanying diagram of isoscelestriangle KLC,

−−−LK ∼=

−−−LC, m∠K = 53, altitude

−−−CA is

drawn to leg−−−LK, and LA = 3. Find the perimeter

of ^KLC to the nearest integer.

page52 Trig Q Bank

636. In the accompanying diagram of rectangle ABCD,diagonal

−−−AC is drawn, DE = 8,

−−−DE ⊥

−−−AC, and

m∠DAC = 55. Find the area of rectangle ABCDto the nearest integer.

637. A 20-foot ladder is leaning against a wall. Thefoot of the ladder makes an angle of 58◦ with theground. Find, to the nearest foot, the verticaldistance from the top of the ladder to the ground.

638. The vertex angle of an isosceles triangle measures56◦ and each leg measures 8. Find the area of thetriangle to the nearest tenth. [Show or explain theprocedure used to obtain your answer.]

639. In the accompanying diagram, the slope of theascent of an aircraft is 7

50 . Find m∠x, the angleof elevation, to the nearest degree.

640. In rectangle ABCD, AD = 10, CD = 8, and diagonal−−−AC is drawn. Find m∠CAD to the nearest degree.

641. In a rectangle, the length of the diagonal is 15 andthe length of the shorter side is 7. Find, to thenearest degree, the number of degrees in the angleformed by the diagonal and the longer side of therectangle.

642. The length of the hypotenuse of a right triangle is2 feet more than the longer leg. The length ofthe longer leg is 7 feet more than the length ofthe shorter leg. Find the number of feet in thelength of each side of the right triangle. [Only analgebraic solution will be accepted. ]

643. The accompanying diagram shows a ramp 30 feetlong leaning against a wall at a construction site.

If the ramp forms an angle of 32◦ with theground, how high above the ground, to the nearesttenth, is the top of the ramp?

A. 15.9 ft B. 18.7 ft C. 25.4 ft D. 56.6 ft

644. Ron and Francine are building a ramp forperforming skateboard stunts, as shown in theaccompanying diagram. The ramp is 7 feet longand 3 feet high. What is the measure of theangle, x, that the ramp makes with the ground, tothe nearest tenth of a degree?

page53 Trig Q Bank

645. From a point on level ground 25 feet from thebase of a tower, the angle of elevation to the topof the tower is 78◦, as shown in the accompanyingdiagram. Find the height of the tower, to thenearest tenth of a foot.

646. A person measures the angle of depression fromthe top of a wall to a point on the ground. Thepoint is located on level ground 62 feet from thebase of the wall and the angle of depression is52◦. How high is the wall, to the nearest tenth ofa foot?

647. A tree casts a shadow that is 20 feet long. Theangle of elevation from the end of the shadow tothe top of the tree is 66◦. Determine the height ofthe tree, to the nearest foot.

648. The accompanying diagram shows a flagpole thatstands on level ground. Two cables, r and s, areattached to the pole at a point 16 feet above theground. The combined length of the two cablesis 50 feet. If cable r is attached to the ground12 feet from the base of the pole, what is themeasure of the angle, x, to the nearest degree, thatcable s makes with the ground?

649. In the accompanying diagram, a ladder leaningagainst a building makes an angle of 58◦ withlevel ground. If the distance from the foot of theladder to the building is 6 feet, find, to the nearestfoot, how far up the building the ladder will reach.

page54 Trig Q Bank

650. In the accompanying diagram, x represents thelength of a ladder that is leaning against a wallof a building, and y represents the distance fromthe foot of the ladder to the base of the wall.The ladder makes a 60◦ angle with the groundand reaches a point on the wall 17 feet above theground. Find the number of feet in x and y.

651. Draw and label a diagram of the path of anairplane climbing at an angle of 11◦ with theground. Find, to the nearest foot, the grounddistance the airplane has traveled when it hasattained an altitude of 400 feet.

652. A ship on the ocean surface detects a sunkenship on the ocean floor at an angle of depressionof 50◦. The distance between the ship on thesurface and the sunken ship on the ocean floor is200 meters. If the ocean floor is level in thisarea, how far above the ocean floor, to the nearestmeter, is the ship on the surface?

653. Find, to the nearest tenth of a foot, the height ofthe tree represented in the accompanying diagram.

654. A 10-foot ladder is to be placed against the sideof a building. The base of the ladder must beplaced at an angle of 72◦ with the level groundfor a secure footing. Find, to the nearest inch,how far the base of the ladder should be from theside of the building and how far up the side ofthe building the ladder will reach.

655. A surveyor needs to determine the distance acrossthe pond shown in the accompanying diagram.She determines that the distance from her positionto point P on the south shore of the pond is175 meters and the angle from her position topoint X on the north shore is 32◦. Determinethe distance, PX, across the pond, rounded to thenearest meter.

page55 Trig Q Bank

656. Mr. Gonzalez owns a triangular plot of land BCDwith DB = 25 yards and BC = 16 yards. Hewishes to purchase the adjacent plot of land inthe shape of right triangle ABD, as shown in theaccompanying diagram, with AD = 15 yards. If thepurchase is made, what will be the total numberof square yards in the area of his plot of land,ÂCD ?

657. A person standing on level ground is 2,000 feetaway from the foot of a 420-foot-tall building,as shown in the accompanying diagram. To thenearest degree, what is the value of x?

658. Joe is holding his kite string 3 feet above theground, as shown in the accompanying diagram.The distance between his hand and a point directlyunder the kite is 95 feet. If the angle of elevationto the kite is 50◦, find the height, h, of his kite, tothe nearest foot.

659. In the accompanying diagram of ÂBC,AB = 12 feet, DC = 17 feet, m∠ABD = 40, andm∠ADB = 110. Find AC to the nearest foot.

page56 Trig Q Bank

660. To determine the distance across a river, asurveyor marked three points on one riverbank: H,G, and F, as shown. She also marked one pointK, on the opposite bank such that

−−−−KH ⊥

−−−−−HGF,

m∠KGH = 41, and m∠KFH = 37. The distancebetween G and F is 45 meters. Find KH, thewidth of the river, to the nearest tenth of a meter.

661. What is the area of a parallelogram if two adjacentsides measure 4 and 5 and an included anglemeasures 60◦?

A. 5√

2 B. 10√

2 C. 5√

3 D. 10√

3

662. An airplane traveling at a level altitude of 2050feet sights the top of a 50-foot tower at anangle of depression of 28◦ from point A. Aftercontinuing in level flight to point B, the angle ofdepression to the same tower is 34◦. Find, to thenearest foot, the distance that the plane traveledfrom point A to point B.

663. A landscape architect is designing a triangulargarden to fit in the corner of a lot. The corner ofthe lot forms an angle of 70◦, and the sides ofthe garden including this angle are to be 11 feetand 13 feet, respectively. Find, to the nearestinteger, the number of square feet in the area ofthe garden.

664. A sign 46 feet high is placed on top of anoffice building. From a point on the sidewalklevel with the base of the building, the angle ofelevation to the top of the sign and the angle ofelevation to the bottom of the sign are 40◦ and32◦, respectively. Sketch a diagram to representthe building, the sign, and the two angles, and findthe height of the building to the nearest foot.

665. To measure the distance through a mountainfor a proposed tunnel, surveyors chose points Aand B at each end of the proposed tunnel anda point C near the mountain. They determinedthat AC = 3,800 meters, BC = 2,900 meters, andm∠ACB = 110. Draw a diagram to illustrate thissituation and find the length of the tunnel, to thenearest meter.

666. A ski lift begins at ground level 0.75 mile fromthe base of a mountain whose face has a 50◦

angle of elevation, as shown in the accompanyingdiagram. The ski lift ascends in a straight line atan angle of 20◦. Find the length of the ski liftfrom the beginning of the ski lift to the top of themountain, to the nearest hundredth of a mile.

page57 Trig Q Bank

667. Kristine is riding in car 4 of the Ferris wheelrepresented in the accompanying diagram. TheFerris wheel is rotating in the direction indicatedby the arrows. The eight cars are equally spacedaround the circular wheel. Express, in radians, themeasure of the smallest angle through which shewill travel to reach the bottom of the Ferris wheel.

668. A student attaches one end of a rope to a wall ata fixed point 3 feet above the ground, as shown inthe accompanying diagram, and moves the otherend of the rope up and down, producing a wavedescribed by the equation y = a sin bx + c. Therange of the rope’s height above the ground isbetween 1 and 5 feet. The period of the wave is4π. Write the equation that represents this wave.

669. A farmer has determined that a crop ofstrawberries yields a yearly profit of $1.50 persquare yard. If strawberries are planted on atriangular piece of land whose sides are 50 yards,75 yards, and 100 yards, how much profit, to thenearest hundred dollars, would the farmer expectto make from this piece of land during the nextharvest?

670. While sailing a boat offshore, Donna sees alighthouse and calculates that the angle ofelevation to the top of the lighthouse is 3◦, asshown in the accompanying diagram. When shesails her boat 700 feet closer to the lighthouse,she finds that the angle of elevation is now 5◦.How tall, to the nearest tenth of a foot, is thelighthouse?

671. A ship captain at sea uses a sextant to sightan angle of elevation of 37◦ to the top of alighthouse. After the ship travels 250 feet directlytoward the lighthouse, another sighting is made,and the new angle of elevation is 50◦. The ship’scharts show that there are dangerous rocks 100 feetfrom the base of the lighthouse. Find, to thenearest foot, how close to the rocks the ship is atthe time of the second sighting.

672. A picnic table in the shape of a regular octagon isshown in the accompanying diagram. If the lengthof−−−AE is 6 feet, find the length of one side of the

table to the nearest tenth of a foot, and find thearea of the table’s surface to the nearest tenth of asquare foot.

673. An art student wants to make a string collageby connecting six equally spaced points on thecircumference of a circle to its center with string.What would be the radian measure of the anglebetween two adjacent pieces of string, in simplestform?

page58 Trig Q Bank

674. Kieran is traveling from city A to city B. As theaccompanying map indicates, Kieran could drivedirectly from A to B along County Route 21 at anaverage speed of 55 miles per hour or travel onthe interstates, 45 miles along I-85 and 20 milesalong I-64. The two interstates intersect at anangle of 150◦ at C and have a speed limit of65 miles per hour. How much time will Kieransave by traveling along the interstates at an averagespeed of 65 miles per hour?

675. Two straight roads, Elm Street and Pine Street,intersect creating a 40◦ angle, as shown in theaccompanying diagram. John’s house (J) is onElm Street and is 3.2 miles from the point ofintersection. Mary’s house (M) is on Pine Streetand is 5.6 miles from the intersection. Find, to thenearest tenth of a mile, the direct distance betweenthe two houses.

676. The accompanying diagram shows the floor planfor a kitchen. The owners plan to carpet all ofthe kitchen except the “work space,” which isrepresented by scalene triangle ABC. Find the areaof this work space to the nearest tenth of a squarefoot.

677. An object that weighs 2 pounds is suspended in aliquid. When the object is depressed 3 feet fromits equilibrium point, it will oscillate according tothe formula x = 3 cos(8t), where t is the numberof seconds after the object is released. How manyseconds are in the period of oscillation?

A. π4 B. π C. 3 D. 2π

678. At Mogul’s Ski Resort, the beginner’s slope isinclined at an angle of 12.3◦, while the advancedslope is inclined at an angle of 26.4◦. If Rudyskis 1,000 meters down the advanced slope whileValerie skis the same distance on the beginner’sslope, how much longer was the horizontaldistance that Valerie covered?

A. 81.3m B. 231.6m

C. 895.7m D. 977.0m

679. A wooden frame is to be constructed in the formof an isosceles trapezoid, with diagonals acting asbraces to strengthen the frame. The sides of theframe each measure 5.30 feet, and the longer basemeasures 12.70 feet. If the angles between thesides and the longer base each measure 68.4◦, findthe length of one brace to the nearest tenth of afoot.

680. Gregory wants to build a garden in the shape ofan isosceles triangle with one of the congruentsides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearest tenthof a degree, the three angles of the triangle.

page59 Trig Q Bank

681. Cassandra is calculating the measure of angle A inright triangle ABC, as shown in the accompanyingdiagram. She knows the lengths of

−−−AB and

−−−BC.

If she finds the measure of angle A by solvingonly one equation, which concept will be used inher calculations?

A. Pythagorean theorem

B. sinA

C. cosA

D. tanA

682. A lighthouse is built on the edge of a cliff nearthe ocean, as shown in the accompanying diagram.From a boat located 200 feet from the base of thecliff, the angle of elevation to the top of the cliffis 18◦ and the angle of elevation to the top ofthe lighthouse is 28◦. What is the height of thelighthouse, x, to the nearest tenth of a foot?

683. The measures of the angles between the resultantand two applied forces are 60◦ and 45◦, and themagnitude of the resultant is 27 pounds. Find, tothe nearest pound, the magnitude of each appliedforce.

684. Akeem invests $25,000 in an account that pays4.75% annual interest compounded continuously.Using the formula A = Pert, where A = the amountin the account after t years, P = principal invested,and r = the annual interest rate, how many years,to the nearest tenth, will it take for Akeem’sinvestment to triple?

A. 10.0 B. 14.6 C. 23.1 D. 24.0

685. An auditorium has 21 rows of seats. The first rowhas 18 seats, and each succeeding row has twomore seats than the previous row. How manyseats are in the auditorium?

A. 540 B. 567 C. 760 D. 798

686. A doctor wants to test the effectiveness of a newdrug on her patients. She separates her sample ofpatients into two groups and administers the drugto only one of these groups. She then comparesthe results. Which type of study best describesthis situation?

A. census

B. survey

C. observation

D. controlled experiment

page60 Trig Q Bank

687. The temperature, T , of a given cup of hotchocolate after it has been cooling for t minutescan best be modeled by the function below, whereT0 is the temperature of the room and k is aconstant.

ln(T − T0) = −kt + 4.718

A cup of hot chocolate is placed in a room thathas a temperature of 68◦. After 3 minutes, thetemperature of the hot chocolate is 150◦. Computethe value of k to the nearest thousandth. [Only analgebraic solution can receive full credit.]

Using this value of k, find the temperature, T , ofthis cup of hot chocolate if it has been sitting inthis room for a total of 10 minutes. Express youranswer to the nearest degree. [Only an algebraicsolution can receive full credit.]

688. The Sea Dragon, a pendulum ride at anamusement park, moves from its central positionat rest according to the trigonometric functionP(t) = −10 sin

( π3 t), where t represents time, in

seconds. How many seconds does it take thependulum to complete one full cycle?

A. 5 B. 6 C. 3 D. 10

689. Al is standing 50 yards from a maple tree and30 yards from an oak tree in the park. Hisposition is shown in the accompanying diagram.If he is looking at the maple tree, he needs to turnhis head 120◦ to look at the oak tree.

How many yards apart are the two trees?

A. 58.3 B. 65.2 C. 70 D. 75

690. The horizontal distance, in feet, that a golf balltravels when hit can be determined by the formula

d =v2 sin 2θ

g, where v equals initial velocity, in

feet per second; g equals acceleration due togravity; equals the initial angle, in degrees, thatthe path of the ball makes with the ground; and dequals the horizontal distance, in feet, that the ballwill travel.

A golfer hits the ball with an initial velocity of180 feet per second and it travels a distance of840 feet. If g = 32 feet per second per second,what is the smallest initial angle the path of theball makes with the ground, to the nearest degree?

691. Jack wants to plant a border of flowers in theshape of an arc along the edge of a circularwalkway. If the circle has a radius of 5 yardsand the angle subtended by the arc measures1 1

2 radians, what is the length, in yards, of theborder?

A. 0.5 B. 2 C. 5 D. 7.5

page61 Trig Q Bank

692. A farmer has a triangular field with sides of240 feet, 300 feet, and 360 feet. He wants toapply fertilizer to the field. If one 40-pound bagof fertilizer covers 6,000 square feet, how manybags must he buy to cover the field?

693. The accompanying diagram shows a triangularplot of land that is part of Fran’s garden. Sheneeds to change the dimensions of this part of thegarden, but she wants the area to stay the same.She increases the length of side AC to 22.5 feet.If angle A remains the same, by how many feetshould side AB be decreased to make the area ofthe new triangular plot of land the same as thecurrent one?

694. The accompanying diagram shows the plans for acell-phone tower that is to be built near a busyhighway. Find the height of the tower, to thenearest foot.

695. As shown in the accompanying diagram, twotracking stations, A and B, are on an east-west line110 miles apart. A forest fire is located at F,on a bearing 42◦ northeast of station A and 15◦

northeast of station B. How far, to the nearestmile, is the fire from station A?

696. The measures of the angles between the resultantand two applied forces are 65◦ and 42◦, and themagnitude of the resultant is 24 pounds. Find, tothe nearest pound, the magnitude of the largerforce.

page62 Trig Q Bank

697. The accompanying diagram shows a resultant forcevector, R.

Which diagram best represents the pair ofcomponent force vectors, A and B, that combinedto produce the resultant force vector R?

A.

B.

C.

D.

698. Two equal forces act on a body at an angle of80◦. If the resultant force is 100 newtons, findthe value of one of the two equal forces, to thenearest hundredth of a newton.

699. One force of 20 pounds and one force of15 pounds act on a body at the same point sothat the resultant force is 19 pounds. Find, to thenearest degree, the angle between the two originalforces.

700. Two tow-trucks try to pull a car out of a ditch.One tow-truck applies a force of 1,500 poundswhile the other truck applies a force of 2,000pounds. The resultant force is 3,000 pounds. Findthe angle between the two applied forces, roundedto the nearest degree.

701. Two forces of 42 pounds and 65 pounds act on abody at an acute angle with each other. The anglebetween the resultant force and the 42-pound forceis 38◦. Find, to the nearest degree, the angleformed by the 42-pound and the 65-pound forces.[Show or explain the procedure used to obtainyour answer.]

702. Two forces act on a body to produce a resultantforce of 70 pounds. One of the forces is50 pounds and forms an angle of 67◦ 40′ with theresultant force. Find, to the nearest pound, themagnitude of the other force. [Show or explainthe procedure used to obtain your answer.]

703. Two forces of 40 pounds and 55 pounds act ona body, forming an acute angle with each other.The angle between the resultant and the 40-poundforce is 22◦ 20′. Find, to the nearest ten minutes,the angle between the two given forces. [Show orexplain the procedure used to obtain your answer.]

704. Two forces of 14 and 30 act on a body forming anobtuse angle with each other. If the resultant forcehas a magnitude of 20, find the angle between thetwo forces to the nearest degree. [Show or explainthe procedure used to obtain your answer.]

page63 Trig Q Bank

Problem-Attic format version 4.4.172c_ 2011–2013 EducAide Software

Licensed for use by Ramesh NairTerms of Use at www.problem-attic.com

Trig Q Bank 04/17/2013

1.Answer: C

2.Answer: A

3.Answer: B

4.Answer: B

5.Answer: D

6.Answer: C

7.Answer: A

8.Answer: C

9.Answer: A

10.Answer: B

11.Answer: A

12.Answer: D

13.Answer: C

14.Answer: A

15.Answer: D

16.Answer: B

17.Answer: B

18.Answer: C

19.Answer: C

20.Answer: A

21.Answer: D

22.Answer: B

23.Answer: A

24.Answer: B

25.Answer: 2.1

26.Answer: B

27.Answer: 37

28.Answer: B

29.Answer: 53

30.Answer: C

31.Answer: B

32.Answer: C

33.Answer: C

34.Answer: A

35.Answer: B

36.Answer: 11.1

37.Answer: A

38.Answer: 11.8

Teacher’s Key Page 2

39.Answer: C

40.Answer: 8.8

41.Answer: C

42.Answer: −

√3

2

43.Answer: A

44.Answer: D

45.Answer: A

46.Answer: 307

47.Answer: B

48.Answer: B

49.Answer: B

50.Answer: B

51.Answer: C

52.Answer: A

53.Answer: C

54.Answer: 45

55.Answer: C

56.Answer: B

57.Answer: D

58.Answer: B

59.Answer: D

60.Answer: OA

61.Answer: D

62.Answer: B

63.Answer: 270

64.Answer: C

65.Answer:

−−−CA

66.Answer: A

67.Answer: D

68.Answer: A

69.Answer: A

70.Answer: D

71.Answer: 3

72.Answer: 9

73.Answer: 2

74.Answer: 15

75.Answer: 2

76.Answer: 3

77.Answer: 2

78.Answer: 7

79.Answer: 5π

80.Answer: 10

81.Answer: C

82.Answer: 2


83.Answer: 5

84.Answer: 12.5

85.Answer: B

86.Answer: 3

87.Answer: 12

88.Answer: 12

89.Answer: 4

90.Answer: 15

91.Answer: 70

92.Answer: 75

93.Answer: 600

94.Answer: C

95.Answer: 210

96.Answer: 252

97.Answer: A

98.Answer: 216

99.Answer: 330

100.Answer: B

101.Answer: 120

102.Answer: B

103.Answer: 540

104.Answer: 40

105.Answer: D

106.Answer: 100

107.Answer: 420

108.Answer: 72

109.Answer: 135

110.Answer: 135

111.

Answer:5π12

112.Answer: 8π

9

113.Answer: 4π

3

114.Answer: 5π

4

115.Answer: 4π

3

116.Answer: 7π

4

117.Answer: 5π

2

118.Answer: 3π

10

119.Answer: 5π

4

120.Answer: π

121.Answer: 4π

3

122.Answer: 2π

3

123.Answer: 7π

6

124.Answer: 8π

9


125.Answer: 5π

3

126.Answer: 4π

3

127.Answer: 8π

9

128.Answer: π

12

129.Answer: 7π

9

130.Answer: 7π

12

131.Answer: A

132.Answer: C

133.Answer: B

134.Answer: D

135.Answer: D

136.Answer: C

137.Answer: B

138.Answer: A

139.Answer: D

140.Answer: D

141.Answer: B

142.Answer: A

143.Answer: B

144.Answer: B

145.Answer: C

146.Answer: D

147.Answer: A

148.Answer: B

149.Answer: C

150.Answer: D

151.Answer: A

152.Answer: A

153.Answer: sin 30◦ or cos 60◦


155.Answer: tan 60◦ or cot 30◦

156.Answer: tan 60◦






162.Answer: 19◦ 33′

163.Answer: 0.7404

164.Answer: 0.5191

165.Answer: 11◦ 15′

166.Answer: C

167.Answer: 0.6116


168.Answer: A

169.Answer: 0.8431

170.Answer: 30◦ 14′

171.Answer: 18

172.Answer: B

173.Answer: 28

174.Answer: 53

175.Answer: 24

176.Answer: 37

177.Answer: 21

178.Answer: C

179.Answer: 52

180.Answer: 13.6

181.Answer: D

182.Answer: C

183.Answer: A

184.Answer: − 5

13

185.Answer: A

186.Answer: −1

187.Answer: B

188.Answer: − 1

2

189.Answer: A

190.Answer: 1

191.Answer: D

192.Answer: 0

193.Answer: C

194.Answer: D

195.Answer: − 4

3

196.Answer: C

197.Answer: A

198.Answer: 1

2

199.Answer: C

200.Answer: 1

201.Answer: B

202.Answer: B

203.Answer: C

204.Answer: B

205.Answer: D

206.Answer: 75◦

207.Answer: 60◦ or π

3

208.Answer: C

209.Answer: 1

2

210.Answer: 30◦


211.Answer: 2√

3

212.Answer: C

213.Answer: B

214.Answer: C

215.Answer: C

216.Answer: 1

217.Answer: 0

218.Answer: A

219.Answer: A

220.Answer: A

221.Answer: C

222.Answer: 60◦ or π

3

223.Answer: 3

5

224.Answer: 1

2

225.Answer: 12

13

226.Answer: 1

2

227.Answer: B

228.Answer: B

229.Answer: 5

12

230.Answer: D

231.Answer: II

232.Answer: C

233.Answer: IV

234.Answer: C

235.Answer: II

236.Answer: D

237.Answer: IV

238.Answer: III

239.Answer: C

240.Answer: B

241.Answer: B

242.Answer: C

243.Answer: C

244.Answer: C

245.Answer: D

246.Answer: C

247.Answer: A

248.Answer: C

249.Answer: IV

250.

Answer:

√2 +√

6

4or

√1 +

√3

2

2

251.Answer: C

252.Answer: B


253.Answer: − 15

17

254.Answer: A

255.Answer: A

256.Answer: D

257.Answer:

√3

2

258.Answer: 3

5

259.Answer: D

260.Answer: 4

5

261.Answer: 2

262.Answer: D

263.Answer: D

264.Answer: C

265.Answer: B

266.Answer: A

267.Answer: B

268.Answer: A

269.Answer: B

270.Answer: D

271.Answer: C

272.Answer: D

273.Answer: D

274.Answer: C

275.Answer: D

276.Answer: D

277.Answer: D

278.Answer: A

279.Answer: 1

280.Answer: A

281.Answer: D

282.Answer: A

283.Answer: A

284.Answer: C

285.Answer: A

286.Answer: D

287.Answer: sin 60◦

288.Answer: C

289.Answer: B

290.Answer: C

291.Answer: C

292.Answer: C

293.Answer: 1

2

294.Answer: D

295.Answer: C


296.Answer: D

297.Answer: C

298.Answer:

√3

2

299.Answer: A

300.Answer: C

301.Answer: A

302.Answer: C

303.Answer: A

304.Answer: C

305.Answer: D

306.Answer: D

307.Answer: D

308.Answer: D

309.Answer: D

310.Answer: 1

9

311.Answer: B

312.Answer: A

313.Answer: 119

169

314.Answer: − 7

25

315.Answer: 7

25

316.Answer: D

317.Answer: 1

9

318.Answer:

√5

5

319.Answer: C

320.Answer: D

321.Answer: D

322.Answer: C

323.Answer: C

324.Answer: C

325.Answer: C

326.Answer: B

327.Answer: D

328.Answer: B

329.Answer: A

330.Answer: D

331.Answer: D

332.Answer: D

333.Answer: A

334.Answer: C

335.Answer: A

336.Answer: A

337.Answer: C

338.Answer: D


339.Answer: C

340.Answer: sin2 θ

341.Answer: A

342.Answer: C

343.Answer: C

344.Answer: D

345.Answer: cosA

346.Answer: C

347.Answer: B

348.Answer: D

349.Answer: B

350.Answer: cos2 θ

351.Answer: D

352.Answer: C

353.Answer: B

354.Answer: B

355.Answer: B

356.Answer: A

357.Answer: A

358.Answer: C

359.Answer: sin2 θ

360.Answer: B

361.Answer: B

362.Answer: C

363.Answer: C

364.Answer: A

365.Answer: B

366.Answer: D

367.Answer: C

368.Answer: D

369.Answer: C

370.Answer: A

371.Answer: D

372.Answer: B

373.Answer: C

374.Answer: B

375.Answer: A

376.Answer: C

377.Answer: C

378.Answer: D

379.Answer: A

380.Answer: D

381.Answer: 18

382.Answer: 150◦


383.Answer: 120

384.Answer: 45

385.Answer: A

386.Answer: 90

387.Answer: B

388.Answer: C

389.Answer: 15

390.Answer: 270◦

391.Answer: 60◦

392.Answer: A

393.Answer: C

394.Answer: C

395.Answer: D

396.Answer: B

397.Answer: 270◦

398.Answer: B

399.Answer: B

400.Answer: C

401.Answer: A

402.Answer: D

403.Answer: 210

404.Answer: 10

405.Answer: 60◦

406.Answer: 15

407.Answer: B

408.Answer: C

409.Answer: C

410.Answer: 60

411.Answer: A

412.Answer: 0 or 0◦

413.Answer: 300

414.Answer: 30

415.Answer: C

416.Answer: B

417.Answer: 240

418.Answer: B

419.Answer: 71, 120, 240, 289

420.Answer: C

421.Answer: 30, 150, 194, 346

422.Answer: 48, 60, 300, 312

423.Answer: 35◦, 77◦, 215◦, 257◦

424.Answer: 42◦, 138◦, 210◦, 330◦

425.Answer: C


426.Answer: B

427.Answer: 70, 169, 250, 349

428.Answer: B

429.Answer: 90◦, 221◦ 50′, 318◦ 10′

430.Answer: 1

431.Answer: 90, 190, 350

432.Answer: A

433.Answer: B

434.Answer: 19, 161, 210, 330

435.Answer: B

436.Answer: 40◦

437.Answer: 3

438.Answer: 60◦, 104.5◦, 255.5◦, 300◦

439.Answer: 78.5 and 281.5

440.Answer: 14.5◦, 165.5◦, 270◦

441.Answer: 9◦ 40′, 170◦ 20′, 270◦

442.Answer: 22.3◦, 157.7◦, 241.5◦, 298.5◦

443.Answer: A

444.Answer: 56.4◦C, 123.6◦C, 270◦C

445.Answer: 228◦40′ and 311◦20′ or 228.6◦ and

311.4◦

446.Answer: 194.5◦, 270◦, 345.5◦ or 194◦ 30′, 270◦,

345◦ 30′.

447.Answer: B

448.Answer: 61, 141, 241, 321

449.Answer: A

450.Answer: B

451.Answer: 111 and 249

452.Answer: 90◦, 221.8◦, 318.2◦

453.Answer: 53.1◦, 306.9◦ or 53◦ 10′, 306◦ 50′

454.Answer: C

455.Answer: 14.5, 165.5, 270 or 14◦30′, 165◦30′,

270◦

456.Answer: 90◦, 194.5◦ (or 194◦ 30′), 270◦, 345.5◦

(or 345◦ 30′)

457.Answer: A

458.Answer: A

459.Answer: 45 and 225

460.Answer: 0,60,180,300

461.Answer: 19, 90, and 161

462.Answer: 60, 109.5, 250.5, 300

463.Answer: 90, 221.81, and 318.19

464.Answer: 90◦ and 270◦


466.Answer: 42, 138, 210, and 330

467.


468.Answer: 44

469.Answer: 30, 150, 270

470.Answer: 210◦ and 330◦

471.Answer: 14.5◦, 90◦, 165.5◦

472.Answer: 109.5◦, 250.5◦

473.Answer: 0.3

474.Answer: 0.2

475.Answer: D

476.Answer: 15

16

477.Answer: 0.4

478.Answer: 2

3

479.Answer: 1

2

480.Answer: 1

3

481.Answer: 4

25

482.Answer: 3

5

483.Answer: 30

484.Answer: 0.5

485.Answer: 1

3

486.Answer: 1

487.Answer: 90

488.Answer: 53

489.Answer: 0.681

490.Answer: 4

5

491.Answer: 3

4

492.Answer: 19

493.Answer: 7

10

494.Answer: 90

495.Answer: A

496.Answer: 16

497.Answer: 6

498.Answer: 16

499.Answer: 40

500.Answer: 4.5

501.Answer: 2.5

502.Answer: 18

503.Answer: C

504.Answer: 4

505.Answer: 24

506.Answer: 8

507.Answer: 38.8

508.Answer: 15

509.Answer: 12


510.Answer: 3

511.Answer: 11 1

4

512.Answer: 8

513.Answer: C

514.Answer: 16

515.Answer: 8

516.Answer: 6.9

517.Answer: 18.1

518.Answer: 7

519.Answer: 8

520.Answer: A

521.Answer: D

522.Answer: 5

523.Answer: B

524.Answer: C

525.Answer: A

526.Answer: 1

527.Answer: B

528.Answer: D

529.Answer: B

530.Answer: A

531.Answer: B

532.Answer: B

533.Answer: A

534.Answer: 2

535.Answer: B

536.Answer: B

537.Answer: B

538.Answer: B

539.Answer: A

540.Answer: C

541.Answer: B

542.Answer: 2

543.Answer: A

544.Answer: B

545.Answer: D

546.Answer: A

547.Answer: B

548.Answer: B

549.Answer: A

550.Answer: Two

551.Answer: B

552.Answer: C

553.Answer: D


554.Answer: B

555.Answer: D

556.Answer: A

557.Answer: C

558.Answer: B

559.Answer: D

560.Answer: B

561.Answer: 14

562.Answer: 6

563.Answer: C

564.Answer: 7

565.Answer: 6

566.Answer: 57

567.Answer: A

568.Answer: B

569.Answer: D

570.Answer: C

571.Answer: 3

7

572.Answer: B

573.Answer: D

574.Answer: C

575.Answer: A

576.Answer: 75

96

577.Answer: D

578.Answer: B

579.Answer: C

580.Answer: B

581.Answer: D

582.Answer: B

583.Answer: A

584.Answer: B

585.Answer: B

586.Answer: 14

587.Answer: D

588.Answer: C

589.Answer: 7

590.Answer: 7

591.Answer: 7

592.Answer: B

593.Answer: 77.9

594.Answer: 8

595.Answer: A

596.Answer: 7


597.Answer: 30

598.Answer: 30

599.Answer: A

600.Answer: C

601.Answer: B

602.Answer: C

603.Answer: 14

604.Answer: 56

605.Answer: 4

√3

606.Answer: 12

√3

607.Answer: 20

√3

608.Answer: 120

609.Answer: 20

610.Answer: 3

√2

611.Answer: 12

612.Answer: B

613.Answer: 18

614.Answer: 9.3

615.Answer: 6

616.Answer: 12 1

2

617.Answer: 7.5

618.Answer: D

619.Answer: 24

620.Answer: 15

621.Answer: C

622.Answer: − 2

7

623.Answer: AB = 330, AC = 330, BC = 295

624.Answer: 109◦ 30′

625.Answer: 11.5

626.Answer: 92

627.Answer: 175

628.Answer: 96◦ 50′

629.Answer: 754

630.Answer: 23

631.Answer: 237

632.Answer: 62.4

633.Answer: B

634.Answer: B

635.Answer: 35

636.Answer: 136

637.Answer: 17

638.Answer: 26.5

639.Answer: 8


640.Answer: 39

641.Answer: 28

642.Answer: 8, 15, 17

643.Answer: A

644.Answer: 25.4

645.Answer: 117.6

646.Answer: 79.4

647.Answer: 45

648.Answer: 32

649.Answer: 10

650.Answer: x = 19.62990915 and y = 9.814954576

651.Answer: 2,058

652.Answer: 153

653.Answer: 28.2

654.Answer: 114′′ (9 feet 6 inches) and 37′′ (3 feet

1 inch)

655.Answer: 109 meters

656.Answer: 270

657.Answer: 12

658.Answer: 116

659.Answer: 16

660.Answer: 254.7

661.Answer: D

662.Answer: 796

663.Answer: 67

664.Answer: 134

665.Answer: 5,513

666.

667.Answer: 5π

4

668.Answer: y = 2 sin 1

2x + 3 or y = −2 sin 12x + 3

669.Answer: 2,700

670.Answer: 91.5

671.Answer: 330

672.Answer: The side equals 2.3 and the area equals

25.5

673.Answer: π

3

674.Answer: 0.15 hour

675.Answer: 3.8

676.Answer: 164.2

677.Answer: A

678.Answer: A

679.Answer: 11.8

680.Answer: 49.8, 65.1, and 65.1

681.Answer: D

682.Answer: 41.4



684.Answer: C

685.Answer: D

686.Answer: D

687.Answer: k = 0.104 and T = 108

688.Answer: B

689.Answer: C

690.Answer: 28

691.Answer: D

692.Answer: 6

693.Answer: 2

694.Answer: 88

695.Answer: 234

696.Answer: 23

697.Answer: A

698.Answer: 65.27

699.Answer: 116

700.Answer: 63

701.Answer: 61◦

702.Answer: 69

703.Answer: 38◦ 20′

704.Answer: 146◦

Documents

Trig Question Bank.pdf