Deck 5: Trigonometric Functions

Question 1

Classify the angle as acute, right, obtuse, or straight.
$94 ^ { \circ }$

A) obtuse
B) right
C) straight
D) acute

Answer 1

A

Question 2

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
$r = \frac { 1 } { 3 }$ feet, $s = 8$ feet

A) 24 radians
B) $\frac { 8 } { 3 }$ radians
C) $24 ^ { \circ }$
D) $\frac { 8 ^ { \circ } } { 3 }$

Answer 2

A

Question 3

Convert the angle in radians to degrees.
$- 54 ^ { \circ }$

A) $- \frac { 3 \pi } { 10 }$ radians
B) $- \frac { 4 \pi } { 11 }$ radians
$C ) - \frac { 2 \pi } { 9 }$ radians
D) $- \frac { 1 } { 5 } \pi$ radians

Answer 3

A

Question 4

Convert the angle in radians to degrees.
$\frac { \pi } { 3 }$

A) $60 ^ { \circ }$
B) $1 ^ { \circ }$
C) $\left( \frac { \pi } { 3 } \right) \circ$
D) $60 \pi ^ { \circ }$

Question 5

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
$\mathrm { r } = 1.7$ meters, $\mathrm { s } = 4.93$ meters

A) $2.9$ radians
B) $0.59$ radians
C) $1.1$ radians
D) $0.85$ radians

Question 6

Convert the angle in degrees to radians. Express answer as a multiple of π.
$- 36 ^ { \circ }$

A) $- \frac { \pi } { 5 }$ radians
B) $- \frac { \pi } { 6 }$ radians
C) $- \frac { \pi } { 7 }$ radians
D) $- \frac { \pi } { 4 }$ radians

Question 7

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
$\mathrm { r } = 7$ inches, $\mathrm { s } = 49$ inches

A) 7 radians
B) $\frac { 1 } { 7 }$ radians
C) $- 7$ radians
D) $7 ^ { \circ }$

Question 8

Classify the angle as acute, right, obtuse, or straight.
$115.891 ^ { \circ }$

A) obtuse
B) acute
C) right
D) straight

Question 9

Classify the angle as acute, right, obtuse, or straight.
$\pi$

A) straight
B) right
C) obtuse
D) acute

Question 10

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
$\mathrm { r } = 1$ meter, $\mathrm { s } = 200$ centimeters

A) 2 radians
B) $\frac { 1 } { 200 }$ radians
C) 200 radians
D) 20 radians

Question 11

Convert the angle in degrees to radians. Express answer as a multiple of π.
$60 ^ { \circ }$

A) $\frac { \pi } { 3 }$ radians
B) $\frac { \pi } { 4 }$ radians
C) $\frac { \pi } { 5 }$ radians
D) $\frac { \pi } { 2 }$ radians

Question 12

Classify the angle as acute, right, obtuse, or straight.
$\frac { \pi } { 5 }$

A) acute
B) right
C) obtuse
D) straight

Question 13

The given angle is in standard position. Determine the quadrant in which the angle lies.
$169 ^ { \circ }$

A) Quadrant II
B) Quadrant I
C) Quadrant III
D) Quadrant IV

Question 14

Classify the angle as acute, right, obtuse, or straight.
$55 ^ { \circ }$

A) acute
B) obtuse
C) straight
D) right

Question 15

The given angle is in standard position. Determine the quadrant in which the angle lies.
$18 ^ { \circ }$

A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV

Question 16

Convert the angle in degrees to radians. Express answer as a multiple of π.
$150 ^ { \circ }$

A) $\frac { 5 \pi } { 6 }$ radians
B) $\frac { 6 \pi } { 7 }$ radians
C) $\frac { 4 \pi } { 5 }$ radians
D) $\frac { 2 } { 3 } \pi$ radians

Question 17

The given angle is in standard position. Determine the quadrant in which the angle lies.
$- 106 ^ { \circ }$

A) Quadrant III
B) Quadrant I
C) Quadrant II
D) Quadrant IV

Question 18

Classify the angle as acute, right, obtuse, or straight.
$\frac { 3 \pi } { 4 }$

A) obtuse
B) straight
C) acute
D) right

Question 19

Classify the angle as acute, right, obtuse, or straight.
23.01

A) acute
B) right
C) obtuse
D) straight

Question 20

The given angle is in standard position. Determine the quadrant in which the angle lies.
$- 39 ^ { \circ }$

A) Quadrant IV
B) Quadrant I
C) Quadrant II
D) Quadrant III

Question 21

Draw Angles in Standard Position
$$- \frac { 3 \pi } { 4 }$$

A)

B)

C)

D)

Question 22

Draw Angles in Standard Position
$- 150 ^ { \circ }$ A)

A)

B)

C)

D)

Question 23

Draw Angles in Standard Position
$- \frac { 7 \pi } { 6 }$

A)

B)

C)

D)

Question 24

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$639 ^ { \circ }$

A) $279 ^ { \circ }$
B) $459 ^ { \circ }$
C) $319.5 ^ { \circ }$
D) $269 ^ { \circ }$

Question 25

Draw Angles in Standard Position
$405 ^ { \circ }$

A)

C)

B)

D)

Question 26

Convert the angle in radians to degrees.
$- \frac { \pi } { 5 }$

A) $- 36 ^ { \circ }$
B) $- 1 ^ { \circ }$
C) $- \left( \frac { \pi } { 5 } \right) ^ { \circ }$
D) $- 36 \pi ^ { \circ }$

Question 27

Draw Angles in Standard Position
$330 ^ { \circ }$

A)

B)

C)

D)

Question 28

Convert the angle in radians to degrees. Round to two decimal places.
$2 \pi$ radians

A) $360 ^ { \circ }$
B) $361 ^ { \circ }$
C) $362 ^ { \circ }$
D) $359 ^ { \circ }$

Question 29

Convert the angle in radians to degrees.
$$\frac { 11 } { 2 } \pi$$

A) $990 ^ { \circ }$
B) $1980 ^ { \circ }$
C) $164 ^ { \circ }$
D) $33 \pi ^ { \circ }$

Question 30

Draw Angles in Standard Position
$60 ^ { \circ }$

A)

B)

C)

D)

Question 31

Draw Angles in Standard Position
$\frac { 13 \pi } { 6 }$

A)

B)

C)

D)

Question 32

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$- 84 ^ { \circ }$

A) $276 ^ { \circ }$
B) $96 ^ { \circ }$
C) $456 ^ { \circ }$
D) $84 ^ { \circ }$

Question 33

Draw Angles in Standard Position
$\frac { 7 \pi } { 4 }$

A)


B)

C)

D)

Question 34

Draw Angles in Standard Position
$\frac { 2 \pi } { 3 }$

A)

B)

C)

D)

Question 35

Convert the angle in radians to degrees. Round to two decimal places.
$- 194 ^ { \circ }$

A) $- 3.39$ radians
B) $- 3.38$ radians
C) $- 3.37$ radians
D) $- 3.36$ radians

Question 36

Draw Angles in Standard Position
$- 120 ^ { \circ }$

A)

B)

C)

D)

Question 37

Convert the angle in radians to degrees.
$\frac { 11 } { 3 } \pi$

A) $660 ^ { \circ }$
B) $1320 \pi ^ { \circ }$
C) $12 ^ { \circ }$
D) $330 ^ { \circ }$

Question 38

Convert the angle in radians to degrees. Round to two decimal places.
2 radians

A) $114.59 ^ { \circ }$
B) $113.67 ^ { \circ }$
C) $0.03 ^ { \circ }$
D) $- 0.16 ^ { \circ }$

Question 39

Convert the angle in radians to degrees. Round to two decimal places.
-6.56 radians

A) $- 375.86 ^ { \circ }$
В) $- 377.08 ^ { \circ }$
C) $- 0.11 ^ { \circ }$
D) $- 0.28 ^ { \circ }$

Question 40

Convert the angle in degrees to radians. Round to two decimal places.
$120 ^ { \circ }$

A) $2.09$ radians
B) $2.08$ radians
C) $2.07$ radians
D) $2.06$ radians

Question 41

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
A pendulum swings through an angle of 20° each second. If the pendulum is 25 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places.

A) 8.73 inches
B) 11.16 inches
C) 10.02 inches
D) 6.88 inches

Question 42

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
$\mathrm { r } = 45$ inches, $\theta = 35 ^ { \circ }$

A) $27.49$ inches
B) $29.92$ inches
C) $28.78$ inches
D) $25.64$ inches

Question 43

Express the angular speed in radians per second.
A carousel has a radius of 18 feet and takes 31 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) $3.65$ feet per second
B) $0.58$ feet per second
C) $10.82$ feet per second
D) $113.1$ feet per second

Question 44

Express the angular speed in radians per second.
A car is traveling at $34 \mathrm { mph }$ . If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

A) $439.56$ revolutions per minute
B) $2761.85$ revolutions per minute
C) $433.56$ revolutions per minute
D) $879.12$ revolutions per minute

Question 45

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
A wheel with a 32-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 14 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

A) $25.1 ^ { \circ }$
B) $27.1 ^ { \circ }$
C) $23.1 ^ { \circ }$
D) $21.1 ^ { \circ }$

Question 46

Express the angular speed in radians per second.
A gear with a radius of 32 centimeters is turning at $\frac { \pi } { 3 }$ radians per sec. What is the linear speed at a point on the outer edge of the gear?

A) $\frac { 32 \pi } { 3 }$ centimeters per second
B) $\frac { 3 \pi } { 32 }$ centimeters per second
C) $96 \pi$ centimeters per second
D) $\frac { \pi } { 96 }$ centimeters per second

Question 47

Express the angular speed in radians per second.
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 415 revolutions per minute? Express the answer in miles per hour rounded to the nearest whole number.

A) 51 miles per hour
B) 8 miles per hour
C) 56 miles per hour
D) 25 miles per hour

Question 48

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
$\mathrm { r } = 10$ centimeters, $\theta = 70 ^ { \circ }$

A) $12.22$ centimeters
B) $13.44$ centimeters
C) 11 centimeters
D) $9.78$ centimeters

Question 49

Express the angular speed in radians per second.
To approximate the speed of a river, a circular paddle wheel with radius $0.48$ feet is lowered into the water. If the current causes the wheel to rotate at a speed of 13 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) $0.45$ miles per hour
B) $0.07$ miles per hour
C) $39.21$ miles per hour
D) $0.22$ miles per hour

Question 50

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.
Find $\cos \theta$

A) $\frac { 3 \sqrt { 34 } } { 34 }$
B) $\frac { \sqrt { 34 } } { 5 }$
C) $\frac { \sqrt { 34 } } { 3 }$
D) $\frac { 5 \sqrt { 34 } } { 34 }$

Question 51

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$\frac { 17 \pi } { 5 }$

A) $\frac { 7 \pi } { 5 }$
B) $- \frac { 17 \pi } { 5 }$
C) $\frac { 12 \pi } { 5 }$
D) $\frac { 3 \pi } { 5 }$

Question 52

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$$- \frac { 2 \pi } { 9 }$$

A) $\frac { 16 \pi } { 9 }$
B) $\frac { 34 \pi } { 9 }$
C) $\frac { 25 \pi } { 9 }$
D) $\frac { 2 \pi } { 9 }$

Question 53

Express the angular speed in radians per second.
420 revolutions per second

A) $840 \pi$ radians per second
B) 840 radians per second
C) $420 \pi$ radians per second
D) 420 radians per second

Question 54

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.

Find $\sin \theta$ .

A) $\frac { 3 \sqrt { 13 } } { 13 }$
B) $\frac { 2 \sqrt { 13 } } { 13 }$
C) $\frac { \sqrt { 13 } } { 3 }$
D) $\frac { \sqrt { 13 } } { 2 }$

Question 55

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
$r = 14.43$ inches, $\theta = 210 ^ { \circ }$

A) $52.89$ inches
B) $52.99$ inches
C) $53.09$ inches
D) $53.19$ inches

Question 56

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$- 893 ^ { \circ }$

A) $187 ^ { \circ }$
B) $533 ^ { \circ }$
C) $173 ^ { \circ }$
D) $7 ^ { \circ }$

Question 57

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 35 minutes? If necessary, round the answer to two decimal places.

A) $14.66$ inches
B) $17.17$ inches
C) $15.89$ inches
D) $12.92$ inches

Question 58

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
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) $214.9 ^ { \circ }$
B) $219.9 ^ { \circ }$
C) $224.9 ^ { \circ }$
D) $229.9 ^ { \circ }$

Question 59

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.

Find $\csc \theta$ .

A) $\frac { \sqrt { 109 } } { 3 }$
B) $\frac { \sqrt { 109 } } { 10 }$
C) $\frac { 3 \sqrt { 109 } } { 109 }$
D) $\frac { 10 \sqrt { 109 } } { 109 }$

Question 60

Find a positive angle less than 360° or 2π that is coterminal with the given angle.
$\frac { 11 \pi } { 5 }$

A) $\frac { \pi } { 5 }$
B) $\frac { 6 \pi } { 5 }$
C) $- \frac { \pi } { 5 }$
D) $\frac { 4 \pi } { 5 }$

Question 61

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\sec 60 ^ { \circ } - \sin 60 ^ { \circ }$

A) $\frac { 4 - \sqrt { 3 } } { 2 }$
B) $\frac { 4 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$
C) $\frac { 4 - \sqrt { 2 } } { 2 }$
D) $\frac { - \sqrt { 3 } } { 6 }$

Question 62

Use the given triangles to evaluate the expression. Rationalize all denominators.
$$\cot \frac { \pi } { 3 } - \sin \frac { \pi } { 3 }$$

A) $- \frac { \sqrt { 3 } } { 6 }$
B) $\sqrt { 3 }$
C) $- \frac { \sqrt { 6 } } { 2 }$
D) $\frac { 2 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$

Question 63

Use the given triangles to evaluate the expression. Rationalize all denominators.
$$\csc \frac { \pi } { 3 }$$

A) $\frac { 2 \sqrt { 3 } } { 3 }$
B) 2
C) $\frac { \sqrt { 3 } } { 2 }$
D) $\sqrt { 2 }$

Question 64

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sin \theta = \frac { 2 } { 7 } , \cos \theta = \frac { 3 \sqrt { 5 } } { 7 }$ . Find $\tan \theta$ .

A) $\frac { 2 \sqrt { 5 } } { 15 }$
B) $\frac { 7 \sqrt { 5 } } { 15 }$
C) $\frac { 2 \sqrt { 5 } } { 2 }$
D) $\frac { 7 } { 2 }$

Question 65

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\cos \frac { \pi } { 6 }$

A) $\frac { \sqrt { 3 } } { 2 }$
B) $\sqrt { 3 }$
C) $\frac { 2 \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 2 } } { 2 }$

Question 66

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.
Find $\sin \theta$ .

A) $\frac { 3 } { 8 }$
B) $\frac { 8 \sqrt { 55 } } { 55 }$
C) $\frac { 3 \sqrt { 55 } } { 55 }$
D) $\frac { \sqrt { 55 } } { 8 }$

Question 67

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.
Find $\cot \theta$ .

A) $\frac { 2 } { 5 }$
B) $\frac { 2 \sqrt { 29 } } { 29 }$
C) $\frac { 5 } { 2 }$
D) $\frac { 5 \sqrt { 29 } } { 29 }$

Question 68

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\csc 30 ^ { \circ }$

A) 2
B) $\frac { 2 \sqrt { 3 } } { 3 }$
C) $\frac { 1 } { 2 }$
D) $\sqrt { 2 }$

Question 69

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sin \theta = - \frac { \sqrt { 5 } } { 3 } , \cos \theta = \frac { 2 } { 3 }$ . Find $\cot \theta$

A) $\frac { - 2 \sqrt { 5 } } { 5 }$
B) $\frac { - 3 \sqrt { 5 } } { 5 }$
C) $\frac { 3 } { 2 }$
D) $\frac { \sqrt { 5 } } { 2 }$ θ is an acute angle and sin θ is given. Use the Pythagorean identity sin2 θ + cos2 θ = 1 to find cos θ.

Question 70

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\sin 60 ^ { \circ }$

A) $\frac { \sqrt { 3 } } { 2 }$
B) $\frac { 1 } { 2 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 2 } } { 2 }$

Question 71

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$$\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$$

A) $\frac { 1 } { 3 }$
B) $2 \sqrt { 2 }$
C) 3
D) $\frac { 3 \sqrt { 2 } } { 4 }$ Use an identity to find the value of the expression. Do not use a calculator.

Question 72

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\sec 45 ^ { \circ }$

A) $\sqrt { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) $\frac { 2 \sqrt { 3 } } { 3 }$
D) $\sqrt { 3 }$

Question 73

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sin ^ { 2 } 20 ^ { \circ } + \cos ^ { 2 } 20 ^ { \circ }$

A) 1
B) 0
C) $0.20$
D) $0.04$

Question 74

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\tan \frac { \pi } { 4 }$

A) 1
B) $\frac { \sqrt { 3 } } { 2 }$
C) $\frac { \sqrt { 2 } } { 2 }$
D) $\sqrt { 2 }$

Question 75

Use the given triangles to evaluate the expression. Rationalize all denominators.
$\csc 60 ^ { \circ } - \sin 45 ^ { \circ }$

A) $\frac { 4 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$
B) $\frac { 4 - \sqrt { 2 } } { 2 }$
C) $\frac { 4 - \sqrt { 3 } } { 2 }$
D) $\frac { 4 \sqrt { 2 } - 3 \sqrt { 3 } } { 6 }$

Question 76

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.
Find $\tan \theta$ .

A) $\frac { 8 } { 7 }$
B) $\frac { 7 } { 8 }$
C) $\frac { \sqrt { 113 } } { 7 }$
D) $\frac { \sqrt { 113 } } { 8 }$

Question 77

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sec ^ { 2 } 50 ^ { \circ } - \tan ^ { 2 } 50 ^ { \circ }$

A) 1
B) 0
C) $0.50$
D) $0.25$

Question 78

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.
Find $\sec \theta$ .

A) $\frac { \sqrt { 149 } } { 7 }$
В) $\frac { 7 \sqrt { 149 } } { 149 }$
C) $\frac { 7 \sqrt { 149 } } { 10 }$
D) $\frac { 10 \sqrt { 149 } } { 149 }$

Question 79

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sin \theta = \frac { 3 } { 7 } , \cos \theta = \frac { 2 \sqrt { 10 } } { 7 } .$ Find $\csc \theta$

A) $\frac { 7 } { 3 }$
B) $\frac { 7 \sqrt { 10 } } { 20 }$
C) $\frac { 2 \sqrt { 10 } } { 3 }$
D) $\frac { 3 \sqrt { 10 } } { 20 }$

Question 80

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
$\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 }$ . Find $\sec \theta$ .

A) $\frac { 4 } { 3 }$
B) $\frac { 4 \sqrt { 7 } } { 7 }$
C) $\frac { 3 \sqrt { 7 } } { 7 }$
D) $\frac { \sqrt { 7 } } { 3 }$