Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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 
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 3

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.

Accepted Answer

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 
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 4

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

Accepted Answer

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 
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 5

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

Accepted Answer

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

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

Accepted Answer

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

Question 7

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 ​

Accepted Answer

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

Question 8

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

Accepted Answer

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° 
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 9

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

Accepted Answer

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

Question 10

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. ​

Accepted Answer

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 
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 11

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
?

Accepted Answer

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

Question 12

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

Accepted Answer

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'' 
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 13

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
?
?

Accepted Answer

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

Question 14

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

Accepted Answer

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' 
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 15

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

Accepted Answer

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 
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 16

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

Accepted Answer

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)  $\frac { 17 \pi } { 6 } , - \frac { 7 \pi } { 6 }$ 
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 17

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

Accepted Answer

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

Question 18

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. ​

Accepted Answer

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 
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 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A) 15° 
B) 10° 
C) 25° 
D) 20° 
E) 55° 
A) 15° 
B) 10° 
C) 25° 
D) 20° 
E) 55°

Exam 23: Radian and Degree Measure

Determine the quadrant in which an angle,?,lies if θ=14π13\theta = \frac { 14 \pi } { 13 }θ=1314π​ .

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

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.

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

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

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

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 ​

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

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

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. ​

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 ?

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

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 ? ?

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

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

Determine two coterminal angles (one positive and one negative)for θ=5π6\theta = \frac { 5 \pi } { 6 }θ=65π​ .

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

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. ​

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

Find angle π9\frac { \pi } { 9 }9π​ in degree measure. ?

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

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

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

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

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

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.

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

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

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

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

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

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.

Find the complement of the following angle. 14°

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