Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side coincides with the positive x-axis.

Question 2

Convert $$75.25^{\circ} to $$degrees, minutes, and seconds.

Accepted Answer

$$75^{\circ} 15$$' 0''$$

Question 3

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

Accepted Answer

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

Question 4

Convert $$120^{\circ} to $$radians.

Accepted Answer

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

Question 5

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

Accepted Answer

$$150^{\circ}$$

Question 6

A camera lens has a viewing angle of $$8^{\circ} 30$$'$$ and is 1000 feet from an object. Approximate the field width imaged by the lens. (Use s = r$$	heta$$ and convert the angle to radians.)

Accepted Answer

148.5 feet

Question 7

Find the area of a sector of a circle with radius 6 meters and a central angle of $$60^{\circ}.$$

Accepted Answer

$$6\pi$$ square meters

Question 8

A child spins a ball at the end of a 3-foot rope at 120 revolutions per minute. What is the linear speed of the ball in feet per minute? (Use $$v = r\omega$$, $$\omega = 2\pi f)$$

Accepted Answer

$$720\pi ft/$$min

Question 9

Which of the following is true about the sign of an angle?

Accepted Answer

Angles measured counterclockwise from the positive x-axis are positive.

Question 10

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

Accepted Answer

$$1$$

Question 11

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

$$5$$ radians

Question 12

Convert $$2.75$$ radians to degrees. (Round to the nearest degree.)

Accepted Answer

$$158^{\circ}$$

Question 13

A Ferris wheel has a radius of 20 meters and rotates at 0.5 revolutions per minute. What is the linear speed of a seat on the edge in meters per minute?

Accepted Answer

$$40\pi m/$$min

Question 14

Which of the following angles is a quadrantal angle?

Accepted Answer

$$270^{\circ}$$

Question 15

A central angle of $$	heta$$ radians in a circle of radius $$r$$ subtends an arc of length $$s. $$Which formula correctly relates these quantities?

Accepted Answer

$$s = r	heta$$

Question 16

If an object moves at a constant angular speed $$\omega on a $$circle of radius $$r$$, what is its linear speed $$v$$?

Accepted Answer

$$v = r\omega$$

Question 17

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

Accepted Answer

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

Question 18

A runner completes one lap around a circular track of radius 50 meters in 40 seconds. What is the runner's angular speed in radians per second?

Accepted Answer

$$\frac{\pi}{20}$$ radians/sec

Question 19

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

Accepted Answer

$$2\pi$$ radians

Question 20

A pizza is cut into 8 equal slices. What is the measure of the central angle for each slice in degrees?

Accepted Answer

$$45^{\circ}$$

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

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