Question 1

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

Accepted Answer

An angle whose terminal side is rotated counterclockwise from the initial side.

Question 2

Convert $$50^  6' 21'' to $$decimal degrees. Round your answer to four decimal places.

Accepted Answer

$$50.1058^ $$

Question 3

A central angle of $$2$$ radians in a circle of radius $$5$$ meters subtends an arc of what length?

Accepted Answer

$$10$$ meters

Question 4

Convert $$120^  to $$radians.

Accepted Answer

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

Question 5

Convert $$\frac{3\pi}{2}$$ radians to degrees.

Accepted Answer

$$270^ $$

Question 6

A Ferris wheel has a radius of $$10$$ meters. What is the length of the arc subtended by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

$$\frac{10\pi}{3}$$ meters

Question 7

Which of the following is the correct formula for the length $$s of an $$arc of a circle of radius $$r$$ subtended by a central angle $$	heta (in $$radians)?

Accepted Answer

$$s = r	heta$$

Question 8

Convert $$21.256^  to $$degrees, minutes, and seconds. Round to the nearest second.

Accepted Answer

$$21^  15' 22''$$

Question 9

A car travels along a circular track of radius $$50$$ meters, subtending a central angle of $$0.4$$ radians. What is the distance traveled by the car?

Accepted Answer

$$20$$ meters

Question 10

Which of the following is equivalent to $$1$$ revolution in radians?

Accepted Answer

$$2\pi$$ radians

Question 11

A clock's minute hand is $$15 cm $$long. How far does the tip of the minute hand travel in $$20$$ minutes?

Accepted Answer

$$10\pi cm$$

Question 12

Convert $$-45^  to $$radians.

Accepted Answer

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

Question 13

Which of the following is the correct relationship between degrees and radians?

Accepted Answer

$$180^  = \pi$$ radians

Question 14

A sector of a circle has a radius of $$8 cm $$and a central angle of $$60^ . $$What is the length of the arc? (Use $$\pi in $$your answer.)

Accepted Answer

$$\frac{8\pi}{3} cm$$

Question 15

If an angle's terminal side lies along the negative $$x-$$axis, what is the measure of the angle in degrees?

Accepted Answer

$$180^ $$

Question 16

A runner completes $$\frac{1}{4} of a $$circular track with a radius of $$40$$ meters. What is the length of the arc the runner covers?

Accepted Answer

$$20\pi$$ meters

Question 17

Convert $$3$$ radians to degrees. Round to the nearest degree.

Accepted Answer

$$172^ $$

Question 18

Which of the following is NOT a correct conversion?

Accepted Answer

$$1' = \frac{1}{3600}^ $$

Question 19

A circular pizza has a radius of $$12$$ inches. If a slice makes a central angle of $$\frac{\pi}{6}$$ radians, what is the length of the crust (arc) of that slice?

Accepted Answer

$$2\pi$$ inches

Question 20

A rotating wheel completes $$3$$ full revolutions. How many radians has it rotated through?

Accepted Answer

$$6\pi$$ radians

Angles, Arc Length, and Circular Motion: Precalculus Study Notes

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