Deck 23: Radian and Degree Measure

Question 1

Find the supplement of the following angle. ​
148°
​

A)Supplement: 212°
B)Supplement: 148°
C)Supplement: 32°
D)Supplement: 58°
E)Supplement: 33

Answer 1

Supplement: 32°

Question 2

Find the quadrant in which the given angle lies. ​
116°
​

A)Quadrant I
B)Quadrant IV
C)Quadrant III
D)Quadrant II
E)None of the above

Answer 2

Quadrant II

Question 3

Convert the angle measure from radians to degrees.Round to three decimal places.? $\frac { 8 \pi } { 13 }$ ?

A) $\frac { 8 \pi } { 13 } = 110.769 ^ { \circ }$
B) $\frac { 8 \pi } { 13 } = 121.269 ^ { \circ }$
C) $\frac { 8 \pi } { 13 } = 105.369 ^ { \circ }$
D) $\frac { 8 \pi } { 13 } = 100.469 ^ { \circ }$
E) $\frac { 8 \pi } { 13 } = 116.369 ^ { \circ }$

Answer 3

$\frac { 8 \pi } { 13 } = 110.769 ^ { \circ }$

Question 4

Find (if possible)the supplement of the following angle.? $\frac { \pi } { 7 }$ ?

A)Supplement: $$\frac { 7 } { 6 \pi }$$
B)Supplement: $- \frac { \pi } { 7 }$
C)Supplement: $\pi$
D)Supplement: $\frac { \pi } { 7 }$
E)Supplement: $\frac { 6 \pi } { 7 }$

Question 5

Find angle 45° in radian measure as a multiple of ?. ?

A) $\frac { 4 \pi } { 3 }$
B) $\frac { \sqrt { 2 } } { \pi }$
C)4?
D) $\frac { \pi } { 4 }$
E) $\frac { \pi \sqrt { 2 } } { 2 }$

Question 6

Find (if possible)the complement of the following angle.? $\frac { \pi } { 3 }$ ?

A)Complement: $$\pi$$
B)Complement: $- \frac { \pi } { 3 }$
C)Complement: $\frac { \pi } { 6 }$
D)Complement: $\frac { \pi } { 3 }$
E)Complement: $\frac { 3 } { \pi }$

Question 7

Convert the angle measure from degrees to radians.Round your answer to three decimal places. ​
90°
​

A)90° ≈ 1.471 radians
B)90° ≈ 9.549 radians
C)90° ≈ 0.090 radian
D)90° ≈ 1.871 radians
E)90° ≈ 1.571 radians

Question 8

Find the quadrant in which the given angle lies. ​
-128° 50'
​

A)Quadrant III
B)Quadrant I
C)Quadrant IV
D)Quadrant II
E)None of the above

Question 9

Find the complement of the following angle.Round your answer to two decimal places. ​
1)1
​

A)Complement ≈ 1.1
B)Complement ≈ 0.47
C)Complement ≈ 4.04
D)Complement ≈ 2.04
E)Complement ≈ 2.51

Question 10

Convert the angle measure from radians to degrees.Round to three decimal places.? $\frac { \pi } { 8 }$ ?

A) $\frac { \pi } { 8 } = 22.5 ^ { \circ }$
B) $\frac { \pi } { 8 } = 27.5 ^ { \circ }$
C) $\frac { \pi } { 8 } = 11.25 ^ { \circ }$
D) $\frac { \pi } { 8 } = 16.25 ^ { \circ }$
E) $\frac { \pi } { 8 } = 57.5 ^ { \circ }$

Question 11

Convert the angle measure from degrees to radians.Round to three decimal places. ​
-0)51°
​

A)-0.51° ≈ -0.309 radian
B)-0.51° ≈ -0.091 radian
C)-0.51° ≈ -0.009 radian
D)-0.51° ≈ -1.309 radians
E)-0.51° ≈ -1.009 radians

Question 12

Find the quadrant in which the given angle lies. ​
-13°
​

A)Quadrant I
B)Quadrant II
C)Quadrant IV
D)Quadrant III
E)None of the above

Question 13

Find angle -20° in radian measure as a multiple of ?. ?

A)9?
B) $\frac { \pi \sqrt { 2 } } { 2 }$
C) $- \frac { \pi } { 9 }$
D) $\frac { \pi \sqrt { 3 } } { 3 }$
E) $\frac { \pi } { 9 }$

Question 14

Find the complement of the following angle. ​
14°
​

A)Complement: 242°
B)Complement: 14°
C)Complement: 76°
D)Complement: 166°
E)Complement: 77°

Question 15

Find angle $\frac { \pi } { 9 }$ in degree measure. ?

A)15°
B)10°
C)25°
D)20°
E)55°

Question 16

Convert the angle measure from degrees to radians.Round to three decimal places. ​
-206.4°
​

A)-206.4° ≈ -3.902 radians
B)-206.4° ≈ -3.502 radians
C)-206.4° ≈ -3.602 radians
D)-206.4° ≈ 3.502 radians
E)-206.4° ≈ 3.602 radians

Question 17

Convert the angle measure from degrees to radians.Round to three decimal places. ​
323°
​

A)323° ≈ 5.637 radians
B)323° ≈ 6.937 radians
C)323° ≈ 5.537 radians
D)323° ≈ 5.937 radians
E)323° ≈ 0.323 radians

Question 18

Convert angle measure to decimal degree form.Round your answer to three decimal places. ​
298°39'
​

A)298°39' ≈ 337°
B)298°39' ≈ 298.39°
C)298°39' ≈ 308.65°
D)298°39' ≈ 298.65°
E)298°39' ≈ 288.65°

Question 19

Convert the angle measure from radians to degrees.Round to three decimal places. ​
-6
​

A)-6 ≈ -354.075°
B)-6 ≈ -349.175°
C)-6 ≈ -343.775°
D)-6 ≈ -333.275°
E)-6 ≈ -338.175°

Question 20

Find angle $\frac { 3 \pi } { 2 }$ in degree measure. ?

A)270°
B)275°
C)145°
D)135°
E)245°

Question 21

Find (if possible)the supplement of $\frac { 3 \pi } { 4 }$ .

A) $\frac { 3 \pi } { 8 }$
B) $\frac { 7 \pi } { 8 }$
C) $\frac { \pi } { 4 }$
D) $\frac { 5 \pi } { 16 }$
E)not possible

Question 22

Rewrite 95° in radian measure as a multiple of ?.? ?

A)? $\frac { 19 \pi } { 12 }$
B)? $\frac { 19 \pi } { 36 }$
C)? $\frac { 19 \pi } { 2 }$
D)? $\frac { 19 \pi } { 6 }$
E)? $\frac { 19 \pi } { 9 }$

Question 23

Find the area of the sector of the circle with radius r and central angle ?.Round to two decimal places. ?
Radius r
Central Angle ?
?4 inches? $\frac { \pi } { 8 }$ ?

A)A ? 12.57 square inches
B)A ? 5.14 square inches
C)A ? 6.28 square inches
D)A ? 1.14 square inches
E)A ? 3.14 square inches

Question 24

Determine two coterminal angles (one positive and one negative)for $\theta = \frac { 5 \pi } { 6 }$ .

A) $\frac { 19 \pi } { 6 } , - \frac { 17 \pi } { 6 }$
B) $\frac { 13 \pi } { 6 } , - \frac { 7 \pi } { 6 }$
C) $\frac { 11 \pi } { 6 } , - \frac { 13 \pi } { 6 }$
D) $\frac { 5 \pi } { 3 } , - \frac { 7 \pi } { 18 }$
E) $\frac { 17 \pi } { 6 } , - \frac { 7 \pi } { 6 }$

Question 25

Convert angle measure to decimal degree form.Round your answer to three decimal places. ​
81° 19' 28''
​

A)81° 19' 28'' ≈ 81.324°
B)81° 19' 28'' ≈ 81.193°
C)81° 19' 28'' ≈ 91.324°
D)81° 19' 28'' ≈ 128°
E)81° 19' 28'' ≈ 71.324°

Question 26

Convert following angle measure to degrees,minutes,and seconds. ​
218)7°
​

A)218.7° ≈ 218°7'
B)218.7° ≈ 218°42'
C)218.7° ≈ 218°40'
D)218.7° ≈ 218°44'
E)218.7° ≈ 218°41'

Question 27

A sprinkler on a golf green is set to spray water over a distance of 12 meters and to rotate through an angle of 130°.Find the area of the region.Round your answer to two decimal places. ​

A)A ≈ 163.36 square meters
B)A ≈ 165.66 square meters
C)A ≈ 161.26 square meters
D)A ≈ 326.73 square meters
E)A ≈ 27.23 square meters

Question 28

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. ​
Radius r
Central Angle θ
15 inches
​123°
​

A)s ≈ 32.20 inches
B)s ≈ 15.68 inches
C)s ≈ 10.25 inches
D)s ≈ 34.20 inches
E)s ≈ 30.20 inches

Question 29

Convert following angle measure to degrees,minutes,and seconds. -328.120°
​

A)-328.120° ≈ -328° 11' ​7''
B)-328.120° ≈ -328° 5' ​16''
C)-328.120° ≈ -328° 7' 11''
D)-328.120° ≈ -328° 16' ​5''
E)-328.120° ≈ -328° 5' 11''

Question 30

Find (if possible)the complement of $\frac { \pi } { 13 }$ .

A) $\frac { 6 \pi } { 13 }$
B) $\frac { 5 \pi } { 13 }$
C) $\frac { 11 \pi } { 26 }$
D)? $\frac { 12 \pi } { 13 }$
E)not possible

Question 31

Find the length of the arc on a circle of radius r intercepted by a central angle θ.Round to two decimal places. ​
Radius r
Central Angle θ
15 centimeters
​66°
​

A)s ≈ 19.28 centimeters
B)s ≈ 15.37 centimeters
C)s ≈ 17.28 centimeters
D)s ≈ 5.50 centimeters
E)s ≈ 15.28 centimeters

Question 32

Determine the quadrant in which an angle with measure 114° lies.

A)4th quadrant
B)2nd quadrant
C)3rd quadrant
D)1st quadrant

Question 33

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. ?
Radius r
Arc Length s
80 kilometers
?145 kilometers
?

A)? = ?6 radians
B)? = $\frac { 29 } { 45 }$ radians
C)? = $\frac { 45 } { 29 }$ radians
D)? = $\frac { 29 } { 16 }$ radians
E)? = ? $\frac { 16 } { 29 }$ radians

Question 34

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. ?
Radius r
Arc Length s
6 inches
?20 inches
?
?

A)? = ?120 radians
B)? = $\frac { 3 } { 10 }$ radians
C)? = $\frac { 3 } { 13 }$ radians
D)? = $\frac { 10 } { 3 }$ radians
E)? = 26 radians

Question 35

Determine the quadrant in which an angle,θ,lies if θ = 5.00 radians.

A)2nd quadrant
B)4th quadrant
C)3rd quadrant
D)1st quadrant

Question 36

Determine the quadrant in which an angle,?,lies if $\theta = \frac { 14 \pi } { 13 }$ .

A)4th quadrant
B)2nd quadrant
C)1st quadrant
D)3rd quadrant

Question 37

Determine two coterminal angles (one positive and one negative)for θ = -489°.

A)141°,-219°
B)321°,-399°
C)231°,-309°
D)141°,-309°
E)231°,-129°

Question 38

Determine the quadrant in which an angle with measure -176°2' lies.

A)3rd quadrant
B)2nd quadrant
C)1st quadrant
D)4th quadrant

Question 39

A carousel with a 60-foot diameter makes 2 revolutions per minute.Find the angular speed of the carousel in radians per minute.Round your answer to two decimal places. ​

A)2 rpm ≈ 61.85 radians per minute
B)2 rpm ≈ 12.57 radians per minute
C)2 rpm ≈ 18.85 radians per minute
D)2 rpm ≈ 6.28 radians per minute
E)2 rpm ≈ 58.23 radians per minute

Question 40

An electric hoist is being used to lift a beam.The diameter of the drum on the hoist is 16 inches,and the beam must be raised 2 feet.Find the number of degrees through which the drum must rotate.Round your answer to nearest whole number.​ ​a = 16,b = 2 ​

A)θ ≈ ​177°
B)θ ≈ ​172°
C)θ ≈ ​162°
D)θ ≈ ​167°
E)θ ≈ ​192°

Question 41

Convert 134°24´40´´ to degree-decimal form.Round answer to three decimal places.

A)134.406°
B)134.411°
C)134.844°
D)134.203°
E)134.206°

Question 42

Rewrite $\frac { 5 \pi } { 3 }$ in degree measure.

A)300°
B)450°
C)600°
D)150°
E)200°

Question 43

Rewrite $\frac { 3 \pi } { 49 }$ in degree measure.Round to three decimal places.

A)11.020°
B)16.531°
C)13.776°
D)3.673°
E)5.510°

Question 44

Find the radian measure of the central angle of the circle of radius 6 centimeters that intercepts an arc of length 32 centimeters.

A) $\theta = \frac { 16 } { 3 }$
B) $\theta = \frac { 2 } { 3 }$
C) $\theta = \frac { 3 } { 16 }$
D) $\theta = \frac { 32 } { 7 }$
E) $\theta = \frac { 6 } { 5 }$

Question 45

A car is traveling along Route 66 at a rate of 55 miles per hour,and the diameter of its wheels are 2.7 feet.Find the number of revolutions per minute the wheels are turning.Round answer to one decimal place.

A)285.3 rpm
B)845.3 rpm
C)570.6 rpm
D)108.1 rpm
E)190.2 rpm

Question 46

Determine the quadrant in which an angle,?,lies if $\theta = \frac { 16 \pi } { 15 }$ .

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 47

Find the length of the arc,S,on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

A)S = 9.42 meters
B)S = 12.57 meters
C)S = 18.85 meters
D)S = 6.28 meters
E)S = 7.54 meters

Question 48

Determine the quadrant in which an angle,θ,lies if θ = 5.10 radians.

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 49

Find the angle,in radians,in the figure below if S = 13 and r = 5.

A) $\frac { 13 \pi } { 5 }$
B) $\frac { 5 } { 13 }$
C) $\frac { 13 } { 5 }$
D) $\frac { 5 \pi } { 13 }$
E) $\frac { 18 \pi } { 5 }$

Question 50

Rewrite -219.80° in radian measure.Round to three decimal places.

A)-0.767
B)-0.691
C)-0.460
D)-0.575
E)-3.836

Question 51

Find the area of the sector of the circle with radius 2 centimeters and central angle $\frac { 10 \pi } { 6 }$ .

A)? $A = \frac { 5 \pi } { 3 } \mathrm {~cm} ^ { 2 }$
B) $A = \frac { 100 \pi } { 3 } \mathrm {~cm} ^ { 2 }$
C) $A = \frac { 10 \pi } { 3 } \mathrm {~cm} ^ { 2 }$
D) $A = \frac { 5 \pi } { 2 } \mathrm {~cm} ^ { 2 }$
E) $A = \frac { 20 \pi } { 3 } \mathrm {~cm} ^ { 2 }$

Question 52

Convert 185.447° to D°M´S´´ form.

A)185°13´25´´
B)185°22´41´´
C)185°20´37´´
D)185°6´12´´
E)185°26´49´´