Trigonometry, 2nd Edition Test Bank

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Trigonometry, 2nd Edition Test Bank makes exam preparation simple with structured and comprehensive questions.

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Ch. 1 Angles and the Trigonometric Functions
1.1 Angles and Radian Measure
1 Recognize and Use the Vocabulary of Angles
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The given angle is in standard position. Determine the quadrant in which the angle lies.
1) -347°
A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV
2) -185°
A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV
3) 203°
A) Quadrant III B) Quadrant I C) Quadrant II D) Quadrant IV
4) -12°
A) Quadrant IV B) Quadrant I C) Quadrant II D) Quadrant III
2 Use Degree Measure
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Classify the angle as acute, right, obtuse, or straight.
1) 36°
A) acute B) obtuse C) straight D) right
2) 134°
A) obtuse B) right C) straight D) acute
3) 5.54°
A) acute B) right C) obtuse D) straight
4) 107.621°
A) obtuse B) acute C) right D) straight
5) π
2
A) right B) straight C) obtuse D) acute
6) π
6
A) acute B) right C) obtuse D) straight
7) 3π
5
A) obtuse B) straight C) acute D) right
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3 Use Radian Measure
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
1) r = 3 inches, s = 21 inches
A) 7 radians B) 1
7 radians C) -7 radians D) 7°
2) r = 1
3 feet, s = 7 feet
A) 21 radians B) 7
3 radians C) 21° D) 7
3
°
3) r = 1.5 meters, s = 2.25 meters
A) 1.5 radians B) 0.67 radians C) 1.4 radians D) 0.75 radians
4) r = 1 meter, s = 400 centimeters
A) 4 radians B) 1
400 radians C) 400 radians D) 40 radians
4 Convert Between Degrees and Radians
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the angle in degrees to radians. Express answer as a multiple of π.
1) 36°
A) π
5 radians B) π
6 radians C) π
7 radians D) π
4 radians
2) -90°
A) - π
2 radians B) - π
3 radians C) - π
4 radians D) - π
8 radians
3) 105°
A) 7π
12 radians B) 8π
13 radians C) 6π
11 radians D) 1
2 π radians
4) - 54°
A) - 3π
10 radians B) - 4π
11 radians C) - 2π
9 radians D) - 1
5 π radians
Convert the angle in radians to degrees.
5) π
4
A) 45° B) 1° C) π
4 ° D) 45π°
6) - π
2
A) -90° B) -2° C) - π
2 ° D) -90π°
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7) 11
2 π
A) 990° B) 1980° C) 164° D) 33π°
8) - 47
18 π
A) -470° B) -940π° C) -8° D) -235°
Convert the angle in degrees to radians. Round to two decimal places.
9) 254°
A) 4.43 radians B) 4.42 radians C) 4.41 radians D) 4.4 radians
10) -73°
A) -1.27 radians B) -1.26 radians C) -1.25 radians D) -1.24 radians
Convert the angle in radians to degrees. Round to two decimal places.
11) 4
3 π radians
A) 240° B) 241° C) 242° D) 239°
12) 2 radians
A) 114.59° B) 113.4° C) 0.03° D) -0.13°
13) -7.81 radians
A) -447.48° B) -446.59° C) -0.14° D) -0.08°
5 Draw Angles in Standard Position
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Draw the angle in standard position.
1) 2π
3
A) B)
C) D)
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2) 512°
A) 152° B) 332° C) 256° D) 142°
3) -1169°
A) 271° B) 809° C) 89° D) 91°
4) 11π
5
A) π
5 B) 6π
5 C) - π
5 D) 4π
5
5) 16π
5
A) 6π
5 B) - 16π
5 C) 11π
5 D) 4π
5
6) - 13π
9
A) 5π
9 B) 23π
9 C) 14π
9 D) 13π
9
7 Find the Length of a Circular Arc
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
1) r = 4 centimeters, θ = 55°
A) 3.84 centimeters B) 4.22 centimeters C) 3.46 centimeters D) 3.07 centimeters
2) r = 50 inches, θ = 45°
A) 39.27 inches B) 41.7 inches C) 40.56 inches D) 37.42 inches
3) r = 12.40 inches, θ = 30°
A) 6.49 inches B) 6.59 inches C) 6.69 inches D) 6.79 inches
Solve the problem.
4) The minute hand of a clock is 7 inches long. How far does the tip of the minute hand move in 50 minutes?
If necessary, round the answer to two decimal places.
A) 36.65 inches B) 39.16 inches C) 37.88 inches D) 34.91 inches
5) A pendulum swings through an angle of 20° each second. If the pendulum is 35 inches long, how far does
its tip move each second? If necessary, round the answer to two decimal places.
A) 12.22 inches B) 14.65 inches C) 13.51 inches D) 10.37 inches
6) A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel
turn when the car rolls forward 5 ft?
A) 214.9° B) 219.9° C) 224.9° D) 229.9°
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7) A wheel with a 40-inch radius is marked at two points on the rim. The distance between the marks along
the wheel is found to be 12 inches. What is the angle (to the nearest tenth of a degree) between the radii to
the two marks?
A) 17.2° B) 19.2° C) 15.2° D) 13.2°
8 Find the Area of a Sector
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round
to two decimal places.
1) r = 6 m, θ = 120°
A) 12π ≈ 37.70 sq m B) 24π ≈ 75.40 sq m
C) 2π ≈ 6.28 sq m D) 2160π ≈ 6785.84 sq m
Find the measure of the central angle on a circle of radius r that forms a sector with the given area, A.
2) r = 7 feet, A = 49 square feet
A) 2 radians B) 14 radians C) 3 radians D) 1 radian
Solve the problem.
3) A lawn sprinkler rotates through an angle of 105° and projects water over a distance of 60 feet. What is the
area of the lawn watered by the sprinkler? Express the answer in terms of π and then round to two
decimal places.
A) 1050π ≈ 3298.67sq ft B) 525π ≈ 1649.34 sq ft
C) 1470π ≈ 4618.14 sq ft D) 2100π ≈ 6597.34 sq ft
9 Use Linear and Angular Speed to Describe Motion on a Circular Path
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the angular speed in radians per second.
1) 420 revolutions per second
A) 840π radians per second B) 840 radians per second
C) 420π radians per second D) 420 radians per second
Solve the problem.
2) A gear with a radius of 32 centimeters is turning at π
9 radians per sec. What is the linear speed at a point
on the outer edge of the gear?
A) 32π
9 centimeters per second B) 9π
32 centimeters per second
C) 288π centimeters per second D) π
288 centimeters per second
3) A car is traveling at 34 mph. If its tires have a diameter of 25 inches, how fast are the car's tires turning?
Express the answer in revolutions per minute. If necessary, round to two decimal places.
A) 457.14 revolutions per minute B) 2872.32 revolutions per minute
C) 439.14 revolutions per minute D) 914.29 revolutions per minute
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4) To approximate the speed of a river, a circular paddle wheel with radius 0.65 feet is lowered into the
water. If the current causes the wheel to rotate at a speed of 12 revolutions per minute, what is the speed of
the current? Express the answer in miles per hour rounded to two decimal places, if necessary.
A) 0.56 miles per hour B) 0.09 miles per hour
C) 49.01 miles per hour D) 0.28 miles per hour
5) A pick-up truck is fitted with new tires which have a diameter of 41 inches. How fast will the pick-up
truck be moving when the wheels are rotating at 335 revolutions per minute? Express the answer in miles
per hour rounded to the nearest whole number.
A) 41 miles per hour B) 7 miles per hour C) 50 miles per hour D) 20 miles per hour
6) A carousel has a radius of 17 feet and takes 25 seconds to make one complete revolution. What is the linear
speed of the carousel at its outside edge? Express the answer in feet per second. If necessary, round the
answer to two decimal places.
A) 4.27 feet per second B) 0.68 feet per second
C) 9.24 feet per second D) 106.81 feet per second
1.2 Right Triangle Trigonometry
1 Use Right Triangles to Evaluate Trigonometric Functions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function
of the given angle. Give an exact answer with a rational denominator.
1) Find sin θ.
8
5
A) 8 89
89 B) 5 89
89 C) 89
8 D) 89
5
2) Find csc θ.
9
10
A) 181
10 B) 181
9 C) 10 181
181 D) 9 181
181
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7) Find sin θ.
10
9
A) 9
10 B) 10 19
19 C) 9 19
19 D) 19
10
2 Find Function Values for 30°(π/6), 45°(π/4), and 60°(π/3)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given triangles to evaluate the expression. Rationalize all denominators.
1) csc 30°
A) 2 B) 2 3
3 C) 1
2 D) 2
2) sec 60°
A) 2 B) 2 3
3 C) 3
2 D) 2
3) cos 45°
A) 2
2 B) 2 C) 3
2 D) 1
2
4) sin π
6
A) 1
2 B) 3
2 C) 3
3 D) 2
2
5) cot π
3
A) 3
3 B) 3 C) 1
2 D) 1
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6) cot π
4
A) 1 B) 2 3
3 C) 2
2 D) 2
7) tan 45° - sin 60°
A) 2 - 3
2 B) 2 3 - 3 2
6 C) 2 - 2
2 D) - 3
6
8) cot 60° - cos 45°
A) 2 3 - 3 2
6 B) 2 - 2
2 C) 2 - 3
2 D) 2 2 - 3 3
6
9) tan π
6 - sin π
3
A) - 3
6 B) 3 C) - 6
2 D) 2 3 - 3 2
6
3 Recognize and Use Fundamental Identities
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
1) sin θ = 5
7 , cos θ = 2 6
7 . Find csc θ.
A) 7
5 B) 7 6
12 C) 2 6
5 D) 5

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Use an identity to find the value of the expression. Do not use a calculator.
6) sin2 70° + cos2 70°
A) 1 B) 0 C) 0.70 D) 0.49
7) sec2 55° - tan2 55°
A) 1 B) 0 C) 0.55 D) 0.30
8) sin 55° csc 55°
A) 1 B) 0 C) 55 D) -1
9) tan 20° - sin 20°
cos 20°
A) 0 B) 1 C) 20 D) Undefined
10) sin 14° csc 14°
A) 1 B) 0 C) 14 D) sin2 14°
11) cos 46° sec 46°
A) 1 B) 0 C) 46 D) cos2 46°
4 Use Equal Cofunctions of Complements
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find a cofunction with the same value as the given expression.
1) sin 67°
A) cos 23° B) cos 67° C) tan 23° D) cot 23°
2) cos 14°
A) sin 76° B) sin 14° C) sec 14° D) csc 76°
3) tan 75°
A) cot 15° B) cot 75° C) sec 75° D) cot 165°
4) csc 5°
A) sec 85° B) sec 5° C) sin 5° D) sec 95°
5) sin π
10
A) cos 2π
5 B) sin 2π
5 C) cos π
10 D) sin π
10
6) cos π
11
A) sin 9π
22 B) cos 9π
22 C) cos π
11 D) sin π
11
7) tan π
14
A) cot 3π
7 B) tan 3π
7 C) cot π
14 D) csc π
14
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8) csc π
13
A) sec 11π
26 B) csc 11π
26 C) cot π
13 D) csc π
13
5 Evaluate Trigonometric Functions with a Calculator
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.
1) sin 27°
A) 0.45 B) 0.51 C) 0.96 D) 0.90
2) cos 17°
A) 0.96 B) 1.04 C) -0.28 D) -0.20
3) cos 5°
A) 1.00 B) -0.28 C) -1.00 D) 0.28
4) tan 72°
A) 3.08 B) 3.01 C) -0.26 D) -0.33
5) csc 40°
A) 1.56 B) 1.46 C) 1.34 D) 1.24
6) cot 0.2038
A) 4.84 B) 0.21 C) 0.98 D) 1.02
7) cot π
7
A) 2.08 B) 2.21 C) 127.66 D) 127.53
8) cos 3π
5
A) -0.31 B) -0.20 C) 1.00 D) 1.11
9) sec π
5
A) 1.24 B) 1.10 C) 1.00 D) 0.86
Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round your
answer to the nearest whole number.
10)
a
36°
b = 11
A) a = 8 cm B) a = 15 cm C) a = 6 cm D) a = 1 cm
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Use a calculator to find the value of the acute angle θ to the nearest degree.
11) tan θ = 13.2894
A) 86° B) 1° C) 88° D) 24°
Use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places.
12) sin θ = 0.8659
A) 1.047 radians B) 59.986 radians C) 5.999 radians D) 0.524 radians
6 Use Right Triangle Trigonometry to Solve Applied Problems
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake
80 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the
angle between the piling and the pier is 30°. What is the distance between the piling and the pier to the
nearest foot?
A) 46 feet B) 40 feet C) 69 feet D) 139 feet
2) A building 150 feet tall casts a 70 foot long shadow. If a person stands at the end of the shadow and looks
up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest
hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level.)
A) 64.23° B) 64.98° C) 61.13° D) 28.87°
3) A radio transmission tower is 120 feet tall. How long should a guy wire be if it is to be attached 11 feet
from the top and is to make an angle of 26° with the ground? Give your answer to the nearest tenth of a
foot.
A) 248.6 feet B) 273.7 feet C) 121.3 feet D) 133.5 feet
4) A straight trail with a uniform inclination of 16° leads from a lodge at an elevation of 500 feet to a
mountain lake at an elevation of 9700 feet. What is the length of the trail (to the nearest foot)?
A) 33,377 feet B) 35,191 feet C) 9571 feet D) 10,091 feet
5) A building 180 feet tall casts a 80 foot long shadow. If a person looks down from the top of the building,
what is the measure of the angle between the end of the shadow and the vertical side of the building (to
the nearest degree)? (Assume the person's eyes are level with the top of the building.)
A) 24° B) 66° C) 64° D) 26°
7 Additional Concepts
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression. Do not use a calculator.
1) 1 + sin2 45° + sin2 45°
A) 2 B) 0 C) -1 D) 1
2) 1 - tan2 75° + csc2 15°
A) 2 B) 0 C) -1 D) 1
3) cos 5°sin 85° + sin 5°cos 85°
A) 1 B) 0 C) -1 D) 2
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4) If tan θ = 11, find the exact value of cot π
2 - θ .
A) 11 B) 1
11 C) 10 D) 12
1.3 Trigonometric Functions of Any Angle
1 Use the Definitions of Trigonometric Functions of Any Angle
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
1) (6, 8) Find sin θ.
A) 4
5 B) 3
5 C) 3
4 D) 4
3
2) (21, 28) Find cos θ.
A) 3
5 B) 4
5 C) 3
4 D) 4
3
3) (-20, 48) Find sin θ.
A) 12
13 B) 5
13 C) - 5
13 D) - 12
13
4) (3, 4) Find csc θ.
A) 5
4 B) 5
3 C) 3
4 D) 4
3
5) (6, 8) Find tan θ.
A) 4
3 B) 3
4 C) 3
5 D) 4
5
6) (3, -4) Find sin θ.
A) - 4
5 B) 3
5 C) 5
3 D) -4
7) (-3, -4) Find sec θ.
A) - 5
3 B) 5
4 C) 4
3 D) - 3
5
8) (- 1
3 , 1
2 ) Find cos θ.
A) - 2 13
13 B) 3 13
13 C) - 13
3 D) 13
2
9) (-9, -4) Find cot θ.
A) 9
4 B) 4
9 C) - 9
10 D) - 2
5
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Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.
10) csc π
A) undefined B) 0 C) -1 D) 1
11) tan π
2
A) undefined B) -1 C) 1 D) 0
2 Use the Signs of the Trigonometric Functions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let θ be an angle in standard position. Name the quadrant in which the angle θ lies.
1) tan θ < 0, sin θ < 0
A) quadrant IV B) quadrant I C) quadrant II D) quadrant III
Find the exact value of the indicated trigonometric function of θ.
2) cos θ = 4
9 , tan θ < 0 Find sin θ.
A) - 65
9 B) - 65
4

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1.4 Trigonometric Functions: The Unit Circle
1 Use a Unit Circle to Define Trigonometric Functions of Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated
trigonometric function at t.
1) 3
4 , 7
4 Find sin t.
A) 7
4 B) 3
4 C) 7
3 D) 3 7
7
2) 5
6 , 11
6 Find tan t.
A) 11
5 B) 6
5 C) 11
6 D) 5 11
11
3) 39
8 , 5
8 Find sec t.
A) 8 39
39 B) 8
5 C) 39
5 D) 5 39
39
4)

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9) 3
4 , - 7
4 Find cos t.
A) 3
4 B) - 7
4 C) 7
4 D) - 3
4
10) 5
7 , - 2 6
7 Find csc t.
A) - 7 6
12 B) 7
5 C) - 6
10 D) 5
7
Use the unit circle to find the value of the trigonometric function.
11) tan π
6
A) 3
3 B) 3 C) 3
2 D) 1
12) tan π
3
A) 3 B) 3
3 C) 3
2 D) 2
13) csc 5π
3
A) - 2 3
3 B) - 3
2 C) 2 D) - 1
2
14) cot 3π
2
A) 0 B) 1 C) -1 D) undefined
2 Recognize the Domain and Range of Sine and Cosine Functions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) What is the domain of the sine function?
A) all real numbers
B) all real numbers from -1 to 1, inclusive
C) all real numbers, except odd multiples of π
2 (90°)
D) all real numbers, except integral multiples of π (180°)
2) What is the range of the cosine function?
A) all real numbers from -1 to 1, inclusive
B) all real numbers
C) all real numbers greater than or equal to 1 or less than or equal to -1
D) all real numbers greater than or equal to 0
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2) The total sales in dollars of some small businesses fluctuates according to the equation S = A + B sin π
6 x,
where x is the time in months, with x = 1 corresponding to January, A = 6700, and B = 4000. Determine the
month with the greatest total sales and give the sales in that month.
A) March; $10,700 B) June; $6700
C) September; $2700 D) December; $10,700
3) The height of the water, H, in feet, at a boat dock t hours after 7 A.M is given by E = 12 + 1.5 cos π
60 t, where
t is time measured in seconds. Find the period.
A) 120 B) π
120 C) 1
120 D) 120π
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Ch. 1 Angles and the Trigonometric Functions
Answer Key
1.1 Angles and Radian Measure
1 Recognize and Use the Vocabulary of Angles
1) A
2) A
3) A
4) A
2 Use Degree Measure
1) A
2) A
3) A
4) A
5) A
6) A
7) A
3 Use Radian Measure
1) A
2) A
3) A
4) A
4 Convert Between Degrees and Radians
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) A
11) A
12) A
13) A
5 Draw Angles in Standard Position
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) A
6 Find Coterminal Angles
1) A
2) A
3) A
4) A
5) A
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6) A
7 Find the Length of a Circular Arc
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8 Find the Area of a Sector
1) A
2) A
3) A
9 Use Linear and Angular Speed to Describe Motion on a Circular Path
1) A
2) A
3) A
4) A
5) A
6) A
1.2 Right Triangle Trigonometry
1 Use Right Triangles to Evaluate Trigonometric Functions
1) A
2) A
3) A
4) A
5) A
6) A
7) A
2 Find Function Values for 30°(π/6), 45°(π/4), and 60°(π/3)
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
3 Recognize and Use Fundamental Identities
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) A
11) A
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4 Use Equal Cofunctions of Complements
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
5 Evaluate Trigonometric Functions with a Calculator
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) A
11) A
12) A
6 Use Right Triangle Trigonometry to Solve Applied Problems
1) A
2) A
3) A
4) A
5) A
7 Additional Concepts
1) A
2) A
3) A
4) A
1.3 Trigonometric Functions of Any Angle
1 Use the Definitions of Trigonometric Functions of Any Angle
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) A
11) A
2 Use the Signs of the Trigonometric Functions
1) A
2) A
3) A
4) A
5) A
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