Test bank for trigonometry 11th edition by lial

Draw the given angle in standard position.. 51 Find the measure of the smaller angle formed by the hands of the clock shown.. 53 54 A surveyor recording data for a new subdivision measur

14) Supplementary angles with measures 2x + 7 and 3x - 2 degrees

A) 57° and 123° B) 77° and 103° C) 67° and 113° D) 87° and 93°

14)

15) Complementary angles with measures 3x and 6x - 18 degrees

A) 66° and 114° B) 38° and 52° C) 12° and 78° D) 36° and 54°

Draw the given angle in standard position Draw an arrow representing the correct amount of rotation Find the measure

of two other angles, one positive and one negative, coterminal with the given angle.

41) 50°

A) 410° and -310° B) 230° and -130°

41)

50)

Solve the problem.

51) Find the measure of the smaller angle formed by the hands of the clock shown

51)

52) A wheel makes 192 revolutions per minute How many revolutions does it make per second?

A) 6.4 revolutions per second B) 3.2 revolutions per secondC) 1152 revolutions per second D) 1.92 revolutions per second

52)

53) A wheel is rotating 240 times per minute Through how many degrees does a point on the edge of

the wheel move in 1

2 seconds?

53)

54) A surveyor recording data for a new subdivision measured an angle as 11.77° The next day, a

different surveyor measured the same angle as 11°31′ Find the difference between thesemeasurements (i) to the nearest minute and (ii) to the nearest hundredth of a degree

54)

55) Determine the measure of the angle in each point of the six-pointed star appearing on police

badges and vehicles (Hint: Inscribe the star in a circle, and use the following theorem from

geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that

cuts off the same arc See the figure.)

70)

70)

71)

71)

72)

72)

73)

73)

74)

75)

Solve the problem Round answers to the nearest tenth if necessary.

96) A tree casts a shadow 38 m long At the same time, the shadow cast by a 37-centimeter-tall statue

is 75 cm long Find the height of the tree

96)

97) A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm The shortest of the

corresponding real-life distances is 92 km Find the longest of the real-life distances

97)

98) Two quadrilaterals (four-sided figures) are similar The lengths of the three longest sides of the

first quadrilateral are 24 ft, 16 ft, and 12 ft The lengths of the two shortest sides of the secondquadrilateral are 18 ft and 9 ft Find the unknown lengths of the sides of these two figures

A) Not enough information is provided

B) The unknown side in the first quadrilateral is 8 ft The two unknown sides in the secondquadrilateral are 36 ft and 12 ft

C) The unknown side in the first quadrilateral is 6 ft The two unknown sides in the secondquadrilateral are 36 ft and 24 ft

D) The unknown side in the first quadrilateral is 10 ft The two unknown sides in the secondquadrilateral are 27 ft and 24 ft

98)

99) An alien observer on Planet X can approximate distances in the sky by using his "hand" at arm's

length An outstretched hand is about 35 arc degrees, a clenched fist is about 25 arc degrees, and athumb corresponds to about 1 arc degree (i) If one clenched fist plus one outstretched hand coversthe distance between two stars, about how far apart in arc degrees are the stars? (ii) The apparentsize of Moon X as observed from Planet X is about 21 arc minutes Approximately what part of anobserver's thumb would cover Moon X?

A) (i) 61 arc degrees; (ii) approximately 1

5 of a thumbB) (i) 50 arc degrees; (ii) approximately 1

4 of a thumbC) (i) 60 arc degrees; (ii) approximately 1

3 of a thumbD) (i) 26 arc degrees; (ii) approximately 1

2 of a thumb

99)

Sketch an angle θ in standard position such that θ has the least positive measure and the given point is on the terminal side of θ.

100) (3, 6)

x

y

x y

100)

101) (-2, 5)

x

y

x y

101)

102) (-5, -3)

x

y

x y

102)

103) (4, -2)

x

y

x y

103)

104) (0, -5)

x

y

x y

104)

105) (-4, 0)

x

y

x y

105)

106) (6, 2)

x

y

x y

106)

107) (-5, 3)

x

y

x y

107)

108) (-2, -7)

x

y

x y

108)

109) (3, -6)

x

y

x y

112)

123) For what angle T is cos T ≈ 0.866? (Assume 0° ≤ T ≤ 90°.)

123)

124) For what angle T is cos T ≈ 0.766? (Assume 0° ≤ T ≤ 90°.)

128) As the cosine increases for 0° ≤ T ≤ 90°, does the sine increase or decrease?

156) tan θ, given that cot θ = - 10

11A) 11

159)

160) csc θ, given that sin θ = 11

6A) 11

160)

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.

161) cos (-283°) and sin (-283°)

161)

162) cos (500°) and tan (500°)

C) positive and negative D) positive and positive

162)

163) csc (559°) and cot (559°)

163)

164) sec (-59°) and sin (-59°)

164)

Identify the quadrant for the angle θ satisfying the following conditions.

165) tan θ > 0 and sin θ < 0

165)

166) cos θ < 0 and csc θ < 0

166)

167) sin θ > 0 and cos θ < 0

167)

168) cot θ < 0 and cos θ > 0

168)

169) csc θ > 0 and sec θ > 0

169)

170) sec θ < 0 and tan θ < 0

170)

171) tan θ < 0 and sin θ < 0

171)

172) cos θ > 0 and csc θ < 0

172)

173) cot θ > 0 and sin θ < 0

173)

174) sin θ > 0 and cos θ > 0

174)

Decide whether the statement is possible or impossible for an angle θ.

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

180) Find sin θ, given that cos θ = 2

3 and θ is in quadrant IV.

180)

181) Find csc θ, given that sin θ = - 2

3 and θ is in quadrant IV.

181)

182) Find tan θ, given that sin θ = 3

4 and θ is in quadrant II.

183)

184) Find cot θ, given that tan θ = 7

3 and θ is in quadrant III.

186) Find tan θ, given that cos θ = -0.25881905 and θ is in quadrant II.

187)

188) Find tan θ, given that sec θ = 3

2 and θ is in quadrant IV.

189) Find cot θ, given that csc θ = - 3

2 and θ is in quadrant III.

189)

190) Find sin θ, given that cos θ = 2

7 and θ is in quadrant IV.

191) Find cos θ, given that tan θ = - 4

3 and θ is in quadrant II.

193)

194) Find cot θ, given that cos θ = 15

17 and θ is in quadrant IV.

195) Find cos θ, given that sin θ = - 5

13 and θ is in quadrant III.