Question 1

A central angle in a circle of radius 5 meters subtends an arc of length 3 meters. What is the measure of the angle in radians?

Accepted Answer

$$0.6$$

Question 2

Convert $$135^{\circ} to $$radians.

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 3

A camera lens has a viewing angle of $$6.13^{\circ}. $$What is this angle in radians? (Round to three decimal places.)

Accepted Answer

$$0.107$$

Question 4

Find the area of a sector of a circle with radius $$3$$ meters and central angle $$45^{\circ}. ($$Round to two decimal places.)

Accepted Answer

$$3.53$$

Question 5

A child spins a rock at the end of a $$2-$$foot rope at $$180$$ revolutions per minute. What is the linear speed of the rock in feet per minute?

Accepted Answer

$$720\pi$$

Question 6

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies on the x-axis or y-axis

Question 7

Convert $$-60^{\circ} to $$radians.

Accepted Answer

$$-\dfrac{\pi}{3}$$

Question 8

If an object moves $$10$$ meters along the circumference of a circle of radius $$4$$ meters, what is the measure of the central angle in radians?

Accepted Answer

$$2.5$$

Question 9

A sector of a circle has an area of $$5$$ square meters and a radius of $$4$$ meters. What is the measure of the central angle in radians?

Accepted Answer

$$0.625$$

Question 10

A wheel of radius $$0.5$$ meters rotates at $$120$$ revolutions per minute. What is the angular speed in radians per minute?

Accepted Answer

$$240\pi$$

Question 11

Which formula gives 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 12

Convert $$\dfrac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^{\circ}$$

Question 13

A Ferris wheel with a radius of $$10$$ meters completes one revolution every $$30$$ seconds. What is the linear speed of a seat on the edge of the wheel in meters per second?

Accepted Answer

$$\dfrac{2\pi 	imes 10}{30}$$

Question 14

Which of the following is true about the relationship between linear speed $$v$$ and angular speed $$\omega$$ for an object moving in a circle of radius $$r$$?

Accepted Answer

$$v = r\omega$$

Question 15

A central angle of $$2$$ radians in a circle of radius $$6$$ meters subtends an arc. What is the length of the arc?

Accepted Answer

$$12$$

Question 16

Convert $$2.5$$ radians to degrees. (Round to the nearest degree.)

Accepted Answer

$$143^{\circ}$$

Question 17

A runner completes a lap around a circular track of radius $$20$$ meters in $$40$$ seconds. What is the runner's angular speed in radians per second?

Accepted Answer

$$\dfrac{2\pi}{40}$$

Question 18

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

Accepted Answer

An angle measured counterclockwise from the positive x-axis

Question 19

A sector of a circle has a central angle of $$\dfrac{\pi}{2}$$ radians and a radius of $$8$$ meters. What is the area of the sector?

Accepted Answer

$$16\pi$$

Chapter 6.1: Angles, Arc Length, and Circular Motion – Precalculus Study Notes

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