Test bank for trigonometry 4th edition by dugopolski

Solve the problem.37 The angle of elevation from the ground to the top of a building is 44.865∘.. Write this angle in the degrees-minutes-seconds format, to the nearest tenth of a second

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

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

Perform the calculation Express the answer in degree-minutes-seconds format.

Solve the problem.

37) The angle of elevation from the ground to the top of a building is 44.865∘ Write this angle in the

degrees-minutes-seconds format, to the nearest tenth of a second

A) 44° 51' B) 42° 51' 54" C) 44° 51' 49" D) 44° 51' 54"

37)

38) The angle between the spokes of a wagon wheel is 19∘ 38' 37" Convert this angle to decimal

degree format (to four decimal places)

56)

57) 4π

5A) 14π

57)

58) 2π

7A) 9π

Draw the angle in standard position.

62) 2π

3A)

B)

C)

D)

62)

68) 12π

5A)- 12π

68)

69) - 3π

10A) 3π

69)

Perform the indicated operation.

70) π

11 + 2πA) 5π

70)

71)- π

6 + 2πA)- π

72)

73) π + π

8A)- π

Solve the problem.

82) On a flywheel with a 62.1-mm radius, how long is an arc subtended by a central angle of 142°?

82)

83) Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger

wheel to rotate The radius of the smaller wheel is 7.2 centimeters and the radius of the largerwheel is 21.5 centimeters Through how many degrees will the larger wheel rotate if the smallerone rotates 131°?

85) The city park district is planning on sodding the outfield of the little league baseball field The

distance from home plate to the outer edge of the infield is 70.00 ft The angle between the outeredge of the first and third baselines is 90°, and the radius of the sector is 235.0 ft Determine thearea of the outfield

235.0 ft

70.00 ft

85)

86) A sensor light installed on the edge of a home can detect motion for a distance of 47 ft in front and

with a range of motion of 206° Over what area will the sensor detect motion and becomeilluminated? Round to two decimal places

90) Express the angular velocity of 900 rad/sec in rev/sec (to the nearest hundredth).

A) 5,654.87 rev/s B) 143.24 rev/s C) 286.48 rev/s D) 2,827.43 rev/s

90)

Solve the problem.

91) Two pulleys of diameter 6 m and 3 m are connected by a belt The larger pulley rotates 46 times

per min Find the angular velocity of the smaller pulley

5π

32 radians/sec

92)

93) A wheel is rotating at 3 radians/sec, and the wheel has a 71-inch diameter To the nearest foot per

minute, what is the linear velocity of a point on the rim?

93)

94) A wheel with a 22-inch diameter is turning at the rate of 34 revolutions per minute To the nearest

inch per minute, what is the linear velocity of a point on the rim?

A) 2396 in./min B) 2403 in./min C) 2350 in./min D) 2357 in./min

94)

95) A satellite in a circular orbit 811.7 mi above the earth makes one complete orbit every 86.43 min

What is its linear velocity? Use 3963 mi for the length of the radius of the earth

A) 412,700 mi/min B) 347.1 mi/min C) 59.01 mi/min D) 55.24 mi/min

95)

96) A pulley with a diameter of 19 inches is driven by a belt which is moving 1089 ft/min To the

nearest unit, how many revolutions per minute are made by the pulley?

100)

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

106) sin 7π

6A) - 1

106)

107) cos 7π

4A) 2

110)

113) cos π

4A) 2

3

12

Find the quadrant that contains the terminal side of angle α.

143) sin α > 0 and cot α > 0

Solve the problem.

151) Find the acute angle α (in degrees) that satisfies the equation sin α = 2

36A) 5

168)

169) Find tan α.

65

25

60A) 5

170)

Solve the right triangle with the given sides and angles.

171) a = 3.8, b = 2.9

A) α = 49.7°, β = 40.3°, c = 6.7 B) α= 37.3°, β = 52.7°, c = 4.8C) α = 48.2°, β = 41.8°, c = 4.8 D) α = 52.7°, β = 37.3°, c = 4.8

171)

172) a = 1.4, β = 42.9°

A) α = 47.1°, b = 2.3, c = 2.7 B) α= 47.1°, b = 2.3, c = 1.9C) α = 47.1°, b = 1.3, c = 1.9 D) α = 47.1°, b = 0.2, c = 1.4

172)

173) a = 3.7, α = 49.1°

A) b = 5.8, β = 40.9°, c = 4.9 B) b = 5.8, β = 40.9°, c = 6.9C) b = 3.2, β = 40.9°, c = 4.9 D) b = 2.1, β = 40.9°, c = 4.3

173)

174) β = 43.9°, c = 3.6

A) a = 2.6, α = 46.1°, b = 1.8 B) a = 2.6, α = 46.1°, b = 2.5C) a = 2.5, α = 46.1°, b = 2.6 D) a = 1.8, α = 46.1°, b = 3.1

174)

Solve the problem.

175) From a boat on the lake, the angle of elevation to the top of a cliff is 21°10' If the base of the cliff is

1268 feet from the boat, how high is the cliff (to the nearest foot)?

175)

176) The angle of elevation from a point on the ground to the top of a tower is 38° 44' The angle of

elevation from a point 117 feet farther back from the tower is 28° 45' Find the height of the tower(to the nearest foot)

176)

177) From a boat on the river below a dam, the angle of elevation to the top of the dam is 15°4' If the

dam is 2492 feet above the level of the river, how far is the boat from the base of the dam (to thenearest foot)?

177)

178) From a balloon 939 feet high, the angle of depression to the ranger headquarters is 80°50' How far

is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

178)

179) When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of

sight is 53°51' If Joey is known to be standing 25 feet from the base of the tree, how tall is the tree(to the nearest foot)?

179)

180) The air speed of an airplane is 580 km/hr and its angle of climb is 1.15° What is its ground speed

(to the nearest km/hr)?

180)

181) At an altitude of 2400 ft, the engine on a small plane fails What angle of depression is needed to

reach an airport runway that is 5 miles away by land? (Round your answer to the nearest tenth of

a degree.)

181)

182) The chairlift at a ski resort has a vertical rise of 2200 feet If the length of the ride is 1.4 miles, what

is the average angle of elevation of the lift (to the nearest tenth of a degree)?

182)

183) Find sin (α), given that cos (α) = 2

9 and α is in quadrant IV.

185)

Draw the angle having the given radian measure.

Use reference angles to find the exact value of the expression.

200) sin 5π

6A) 3

202)

203) cos 7π

6A) - 1

Solve.

213) The ferris wheel at an amusement park is 49 ft in diameter, turns at a rate of 8 rpm, and is 5 ft off

the ground at the low point What is the height of a passenger 20 seconds into the ride?

213)

214) A weight on a vertical spring is given an initial downward velocity of 2 cm/sec from a point 5 cm

above equilibrium Assuming that the constant ω has a value of 2, find the location of the weight 2sec after it is set in motion

A) 3.1 cm below the equilibrium position B) 2.5 cm below the equilibrium positionC) 2.5 cm above the equilibrium position D) 1.8 cm below the equilibrium position

214)

215) The formula d = 1

32 v02 sin (2θ) gives the distance d in feet that a projectile will travel when itslaunch angle is θ and its initial velocity is v0 feet per second Approximately what initial velocity

in miles per hour does it take to throw a javelin 330 feet with a launch angle 43°?

215)