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 $$135^	ext{o} to $$radians.

Accepted Answer

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

Question 3

A camera lens has a viewing angle of $$6^	ext{o}9'$$ and is 725 feet from an object. What is the field width (arc length) imaged by the lens? (Use $$6^	ext{o}9' = 0.1074$$ radians.)

Accepted Answer

$$77.9$$ feet

Question 4

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

Accepted Answer

$$143^	ext{o}$$

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? (Use $$v = r\omega$$ and $$\omega = 2\pi 	imes 180$$ radians/minute.)

Accepted Answer

$$2262 ft/$$min

Question 6

Find the area of a sector of a circle with radius $$3$$ meters and central angle $$45^	ext{o}. ($$Use $$A = \frac{1}{2} r^2$ 	heta$$ with $$	heta in $$radians.)

Accepted Answer

$$3.53$$ square meters

Question 7

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 8

Convert $$65^	ext{o}9'17'' to $$decimal degrees. Round to four decimal places.

Accepted Answer

$$65.1547^	ext{o}$$

Question 9

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

Accepted Answer

$$4\pi$$ radians/second

Question 10

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 11

Convert $$-60^	ext{o} to $$radians.

Accepted Answer

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

Question 12

A sector of a circle has an area of $$10$$ square meters and a radius of $$4$$ meters. What is the measure of the central angle in radians?

Accepted Answer

$$1.25$$

Question 13

If an object travels $$15$$ meters along the circumference of a circle of radius $$3$$ meters, what is the measure of the central angle in radians?

Accepted Answer

$$5$$

Question 14

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

Accepted Answer

$$180^	ext{o} = \pi$$ radians

Question 15

A car tire with a radius of $$0.3$$ meters rotates at $$600$$ revolutions per minute. What is the linear speed of a point on the edge of the tire in meters per minute?

Accepted Answer

$$360\pi$$ meters/minute

Angles, Arc Length, and Circular Motion: Study Notes for Precalculus (Trigonometric Functions)

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