Question 1

A Ferris wheel makes one complete revolution, rotating counterclockwise. What is the measure of the angle in degrees and radians that the wheel has turned?

Accepted Answer

$360\degree$ and $2\pi$ radians

Question 2

Which of the following angles is a quadrantal angle?

Accepted Answer

$90\degree$

Question 3

Convert $-135\degree$ to radians.

Accepted Answer

$-\frac{3\pi}{4}$

Question 4

A clock’s minute hand is 6 inches long. How far does the tip of the minute hand travel in 20 minutes?

Accepted Answer

$4.19$ inches

Question 5

Convert $\frac{7\pi}{6}$ radians to degrees.

Accepted Answer

$210\degree$

Question 6

Find the length of the arc of a circle of radius $70$ meters subtended by a central angle of $35\degree$. Express your answer in decimal form rounded to two decimal places.

Accepted Answer

$35.71$ meters

Question 7

Which formula is used to find the area $A$ of a sector of a circle with radius $r$ and central angle $	heta$ in radians?

Accepted Answer

$A = \frac{1}{2} r 	heta$

Question 8

A sector of a circle has an area of $21$ square miles and is determined by a central angle of $1.2$ radians. What is the radius of the circle? (Round to two decimal places)

Accepted Answer

$5.93$ miles

Question 9

Convert $3.6$ radians to degrees. (Express your answer in decimal form rounded to two decimal places)

Accepted Answer

$171.89\degree$

Question 10

A central angle $	heta$ in a circle of radius $12$ inches subtends an arc of length $5$ inches. What is $	heta$ in radians?

Accepted Answer

$0.42$ radians

Question 11

Which of the following best describes a negative angle in standard position?

Accepted Answer

Its terminal side is rotated clockwise from the initial side.

Question 12

Convert $270\degree$ to radians.

Accepted Answer

$\frac{3\pi}{2}$

Question 13

A pizza with a radius of $8$ inches is cut into a sector with a central angle of $30\degree$. What is the area of the sector? (Round to two decimal places)

Accepted Answer

$16.76$ in$^2$

Question 14

Which of the following is the correct conversion factor from degrees to radians?

Accepted Answer

$1\degree = \frac{\pi}{180}$ radians

Question 15

A central angle of $45\degree$ in a circle of radius $50$ miles subtends an arc. What is the length of the arc? (Round to two decimal places)

Accepted Answer

$39.27$ miles

Question 16

Which of the following angles is in quadrant II?

Accepted Answer

$135\degree$

Question 17

If a central angle of $\frac{\pi}{2}$ radians is drawn in standard position, what is its measure in degrees?

Accepted Answer

$90\degree$

Question 18

A circular running track has a radius of $20$ meters. What is the length of the arc subtended by a central angle of $120\degree$?

Accepted Answer

$41.89$ meters

Question 19

Which of the following is the correct formula for arc length $s$ of a circle with radius $r$ and central angle $	heta$ in radians?

Accepted Answer

$s = r 	heta$

Question 20

A central angle of $420\degree$ is equivalent to which angle between $0\degree$ and $360\degree$?

Accepted Answer

$60\degree$

Angles and Their Measure: Degrees, Radians, Arc Length, and Sector Area

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