Deck 5: The Trigonometric Functions

Question 1

Name the quadrant in which the angle lies.
-301°

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

Answer 1

I

Question 2

Determine whether the angles in the given pair are coterminal.

A) Yes
B) No

Answer 2

Yes

Question 3

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
63°

A) 423°; -117°
B) 243°; -117°
C) 153°; -27°
D) 423°; -297°

Answer 3

423°; -297°

Question 4

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
210°

A) 570°; -150°
B) 390°; -150°
C) 570°; -240°
D) 480°; -60°

Question 5

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

A)
B)
C)
D)

Question 6

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-237°

A) 123°; -417°
B) 33°; -507°
C) 123°; -597°
D) -777°; -597°

Question 7

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
119°

A) 479°; -61°
B) 299°; -61°
C) 479°; -241°
D) 389°; -151°

Question 8

Determine whether the angles in the given pair are coterminal.
127°, 1597°

A) Yes
B) No

Question 9

Determine whether the angles in the given pair are coterminal.
131°, 851°

A) Yes
B) No

Question 10

Determine whether the angles in the given pair are coterminal.
0°, 360.3°

A) Yes
B) No

Question 11

Determine whether the angles in the given pair are coterminal.

A) Yes
B) No

Question 12

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

A)
B)
C)
D)

Question 13

Determine whether the angles in the given pair are coterminal.

A) Yes
B) No

Question 14

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

A)
B)
C)
D)

Question 15

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-93°

A) 267°; -273°
B) 87°; -183°
C) 267°; -453°
D) 87°; -273°

Question 16

Determine whether the angles in the given pair are coterminal.

A) Yes
B) No

Question 17

Determine whether the angles in the given pair are coterminal.
143.8°, -576.2°

A) Yes
B) No

Question 18

Name the quadrant in which the angle lies.
111°

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

Question 19

Determine whether the angles in the given pair are coterminal.

A) Yes
B) No

Question 20

Determine whether the angles in the given pair are coterminal.
95°, -245°

A) Yes
B) No

Question 21

Determine the degree measure of the given angle.

A) 120°
B) 150°
C) 60°
D) 30°

Question 22

Determine the degree measure of the given angle.

A) 45°
B) 60°
C) 30°
D) 120°

Question 23

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-61°56'55''

A) -61.89°
B) -61.99°
C) -61.94°
D) -61.95°

Question 24

Find the angle of smallest possible positive measure that is coterminal with the given angle.
566°

A) 283°
B) 196°
C) 386°
D) 206°

Question 25

Name the quadrant in which the angle lies.
30.2

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

Question 26

Find the angle of smallest possible positive measure that is coterminal with the given angle.

A)
B)
C)
D)

Question 27

Name the quadrant in which the angle lies.
858°

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

Question 28

Name the quadrant in which the angle lies.
-652°

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

Question 29

Determine the degree measure of the given angle.

A) 135°
B) 60°
C) 120°
D) 45°

Question 30

Find the angle of smallest possible positive measure that is coterminal with the given angle.

A)
B)
C)
D)

Question 31

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-104°53'37''

A) -104.83°
B) -104.88°
C) -104.89°
D) -104.93°

Question 32

Name the quadrant in which the angle lies.
1349°

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

Question 33

Find the angle of smallest possible positive measure that is coterminal with the given angle.

A)
B)
C)
D)

Question 34

Determine the degree measure of the given angle.

A) 60°
B) 30°
C) 120°
D) 150°

Question 35

Name the quadrant in which the angle lies.

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

Question 36

Find the angle of smallest possible positive measure that is coterminal with the given angle.
-292°

A) 248°
B) -112°
C) 292°
D) 68°

Question 37

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
54°19'41''

A) 54.29°
B) 54.34°
C) 54.39°
D) 54.33°

Question 38

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
154°15'37''

A) 154.32°
B) 154.26°
C) 154.22°
D) 154.27°

Question 39

Find the angle of smallest possible positive measure that is coterminal with the given angle.

A)
B)
C)
D)

Question 40

Find the angle of smallest possible positive measure that is coterminal with the given angle.
-11.18

A) 4.53
B) 7.67
C) 1.39
D) -1.76

Question 41

Convert the degree measure to radian measure. Give the exact answer.
1080°

A)
B)
C)
D)

Question 42

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
253°9'13''

A) 253.21°
B) 253.11°
C) 253.16°
D) 253.15°

Question 43

Convert the degree measure to radian measure. Give the exact answer.
30°

A)
B)
C)
D)

Question 44

Convert the degree measure to radian measure. Give the exact answer.
-450°

A)
B)
C)
D)

Question 45

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
93.88°

A) 93°52'36''
B) 93°52'54''
C) 93°52'48''
D) 93°52'88''

Question 46

Convert the degree measure to radian measure. Use the value of found on a calculator and round as indicated.
Round to the nearest hundredth of a radian. 9.6°

A) 0.15
B) 0.17
C) 0.18
D) 0.16

Question 47

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
-123.53°

A) -123°31'40''
B) -123°31'48''
C) -123°40'53''
D) -123°31'52''

Question 48

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-356°13'41''

A) -356.27°
B) -356.23°
C) -356.22°
D) -356.17°

Question 49

Convert the degree measure to radian measure. Use the value of found on a calculator and round as indicated.
Round to the nearest thousandth of a radian. 114.5°

A) 1.998
B) 0.5
C) 359.712
D) 3.997

Question 50

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
123.16°

A) 123°9'16''
B) 123°9'36''
C) 123°10'36''
D) 123°7'16''

Question 51

Convert the degree measure to radian measure. Give the exact answer.
390°

A)
B)
C)
D)

Question 52

Convert the degree measure to radian measure. Give the exact answer.
470°

A)
B)
C)
D)

Question 53

Convert the degree measure to radian measure. Give the exact answer.
324°

A)
B)
C)
D)

Question 54

Convert the degree measure to radian measure. Give the exact answer.
450°

A)
B)
C)
D)

Question 55

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
-71.76°

A) -71°55'36''
B) -71°55'26''
C) -71°45'26''
D) -71°45'36''

Question 56

Convert the degree measure to radian measure. Use the value of found on a calculator and round as indicated.
Round to the nearest thousandth of a radian. 99°42'16''

A) 3.48
B) 99.704
C) 1.735
D) 1.74

Question 57

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
-331.51°

A) -331°35'51''
B) -331°30'36''
C) -331°30'51''
D) -331°31'35''

Question 58

Convert the degree measure to radian measure. Give the exact answer.
-30°

A)
B)
C)
D)

Question 59

Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
213°

A) 212°59'0''
B) 212°60'58''
C) 212°58'0''
D) 212°59'59''

Question 60

Convert the degree measure to radian measure. Use the value of found on a calculator and round as indicated.
Round to the nearest hundredth of a radian. 205°18'

A) 3.58
B) 3.55
C) 3.56
D) 3.57

Question 61

Find the corresponding angle measure in radians.

A)
B)
C)
D)

Question 62

Solve the problem.
Find the length of the arc intercepted by a central angle of in a circle of radius 7 cm. Round to two decimal places.

A) 9.77 cm
B) 0.1 cm
C) 10.03 cm
D) 4.89 cm

Question 63

Solve the problem.
Find the radian measure of the central angle which intercepts a 16.5 cm arc in a circle of radius 3 cm. Round to one decimal place, if necessary.

A) 6 radians
B) 5.5 radians
C) 0.1 radians
D) 5 radians

Question 64

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
0.9884

A) 57.13°
B) 55.93°
C) 57.63°
D) 56.63°

Question 65

Solve the problem.
Find the radian measure of the central angle which intercepts a 6 cm arc in a circle of radius 2 cm. Round to one decimal place, if necessary.

A) 2 radians
B) 3 radians
C) 4 radians
D) 0.3 radians

Question 66

Solve the problem.
Use the formula to determine the value of r in the figure. Round to two decimal places.

A) 2.12 ft
B) 0.04 ft
C) 0.47 ft
D) 47.12 ft

Question 67

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
2

A) 114.99°
B) 228.78°
C) 114.59°
D) 229.18°

Question 68

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.

A) -1.05°
B)
C) -60°
D)

Question 69

Solve the problem.
Find the length of the arc intercepted by a central angle of 264° in a circle of radius 6 mi. Round to two decimal places, if necessary.

A) 0.77 mi
B) 1.3 mi
C) 27.65 mi
D) 1584 mi

Question 70

Solve the problem.
Use the formula to determine the value of s in the figure. Round to two decimal places.

A) 18.85 in.
B) 9.42 in.
C) 515.66 in.
D) 0.12 in.

Question 71

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.

A)
B) 7.5°
C) 215°
D) 430°

Question 72

Solve the problem.
A pulley rotates through 57° in one minute. How many rotations does the pulley make in an hour?

A) 342.0 rotations
B) 19.0 rotations
C) 9.5 rotations
D) 171.0 rotations

Question 73

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.

A) 405°
B)
C) 160°
D) 810°

Question 74

Solve the problem.
Use the formula to determine the value of s in the figure. Round to two decimal places, if necessary.

A) 4.46 in.
B) 630 in.
C) 11 in.
D) 1.57 in.

Question 75

Solve the problem.
A bicycle wheel rotates 54 times in 1 minute. Through how many degrees does a point on the tip of the wheel move in 15 seconds?

A) 810°
B) 90°
C) 324°
D) 4860°

Question 76

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.

A)
B)
C) 1.047°
D) 60°

Question 77

Find the corresponding angle measure in radians.

A)
B)
C)
D)

Question 78

Solve the problem.
Use the figure below to determine the radian measure of angle Round to two decimal places, if necessary.

A) 3 radians
B) 0.33 radians
C) 1.5 radians
D) 48 radians

Question 79

Solve the problem.
Use the formula to determine the value of r in the figure. Round to two decimal places.

A) 21.55 ft
B) 16.75 ft
C) 0.06 ft
D) 0.29 ft

Question 80

Solve the problem.
A car wheel has a 15-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 1 ft?

A) 45.8°
B) 60.8°
C) 50.8°
D) 55.8°