Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) 300° 
B) 450° 
C) 600° 
D) 150° 
E) 200° 
A) 300° 
B) 450° 
C) 600° 
D) 150° 
E) 200° A

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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? $\frac { \pi } { 8 }$ ?

Accepted Answer

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 
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 6

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

Accepted Answer

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

Question 7

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

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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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 
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 10

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

Accepted Answer

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)  $A = \frac { 20 \pi } { 3 } \mathrm {~cm} ^ { 2 }$ 
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 11

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

Accepted Answer

A)  $\theta = \frac { 16 } { 3 }$ 
B)  $\theta = \frac { 2 } { 3 }$ 
C)  $\theta = \frac { 3 } { 16 }$ 
D)  $\theta = \frac { 32 } { 7 }$ 
E)  $\theta = \frac { 6 } { 5 }$ 
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 12

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.

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Convert 185.447° to D°M´S´´ form.

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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)  $\frac { \pi } { 8 } = 57.5 ^ { \circ }$ 
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 19

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°
​

Accepted Answer

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 
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 20

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

Accepted Answer

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

Exam 23: Radian and Degree Measure

Find (if possible)the supplement of 3π4\frac { 3 \pi } { 4 }43π​ .

Rewrite 5π3\frac { 5 \pi } { 3 }35π​ in degree measure.

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

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

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? π8\frac { \pi } { 8 }8π​ ?

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

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

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

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

Find the area of the sector of the circle with radius 2 centimeters and central angle 10π6\frac { 10 \pi } { 6 }610π​ .

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

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.

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

Rewrite 3π49\frac { 3 \pi } { 49 }493π​ in degree measure.Round to three decimal places.

Convert 185.447° to D°M´S´´ form.

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

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

Convert the angle measure from radians to degrees.Round to three decimal places.? π8\frac { \pi } { 8 }8π​ ?

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° ​

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

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Introduction to Conics Parabolas

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

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

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

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? $\frac { \pi } { 8 }$ ?

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

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

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

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

Find the supplement of the following angle. 148°

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

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°

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