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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