Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245° 
A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245°

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

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

Accepted Answer

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)  $\frac { 8 \pi } { 13 } = 116.369 ^ { \circ }$ 
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)  $\frac { 8 \pi } { 13 } = 116.369 ^ { \circ }$

Question 7

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°
​

Accepted Answer

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 
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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Exam 23: Radian and Degree Measure

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

Determine the quadrant in which an angle,?,lies if θ=16π15\theta = \frac { 16 \pi } { 15 }θ=1516π​ .

Find angle 3π2\frac { 3 \pi } { 2 }23π​ in degree measure. ?

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

Find (if possible)the supplement of the following angle.? π7\frac { \pi } { 7 }7π​ ?

Convert the angle measure from radians to degrees.Round to three decimal places.? 8π13\frac { 8 \pi } { 13 }138π​ ?

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° ​

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

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

Find (if possible)the complement of π13\frac { \pi } { 13 }13π​ .

Find (if possible)the complement of the following angle.? π3\frac { \pi } { 3 }3π​ ?

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

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