Q: Which of the following is the correct formula for the area $$A of a $$sector of a circle of radius $$r$$ and central angle $$\theta (in $$radians)?

$$A = \frac{1}{2} r^2$ \theta$$

Q: Which of the following statements about angular speed $$\omega is $$correct?

$$\omega = \frac{\theta}{t}$$, where $$\theta is in $$radians and $$t is $$time

Question 1

A central angle in a circle of radius 5 meters subtends an arc of length 8 meters. What is the measure of the angle in radians?

Accepted Answer

$$1.6$$

Question 2

Convert $$120^	ext{o} to $$radians.

Accepted Answer

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

Question 3

A Ferris wheel has a radius of 10 meters. If a seat travels through a central angle of $$\frac{\pi}{4}$$ radians, what is the length of the arc the seat travels?

Accepted Answer

$$\frac{10\pi}{4}$$ meters

Question 4

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

Accepted Answer

$$143^	ext{o}$$

Question 5

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 6

Find the area of a sector of a circle with radius 6 cm and central angle $$60^	ext{o}.$$

Accepted Answer

$$6\pi cm$^2$$

Question 7

A car tire has a radius of 0.3 meters and 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

Question 8

Convert $$75.5^	ext{o} to $$degrees, minutes, and seconds.

Accepted Answer

$$75^	ext{o} 30' 0''$$

Question 9

The latitude of City A is $$40^	ext{o} N $$and City B is $$55^	ext{o} N. If $$both cities are on the same longitude and the radius of Earth is 6371 km, what is the distance between the two cities along the surface of the Earth?

Accepted Answer

$$1672 km$$

Question 10

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 11

A child is spinning a rock at the end of a 2-foot rope at 180 revolutions per minute. What is the angular speed in radians per minute?

Accepted Answer

$$360\pi$$ radians/minute

Question 12

If an object moves along a circle of radius $$r$$ and sweeps out an angle $$	heta (in $$radians) in time $$t$$, what is the formula for its linear speed $$v$$?

Accepted Answer

$$v = \frac{r	heta}{t}$$

Question 13

Which of the following is equivalent to $$1$$ radian?

Accepted Answer

The angle subtended by an arc equal in length to the radius of the circle

Question 14

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

Accepted Answer

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

Question 15

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 16

If the terminal side of an angle in standard position lies in quadrant IV, which of the following could be its measure?

Accepted Answer

$$-45^	ext{o}$$

Question 17

Which of the following is the correct formula for the area $$A of a $$sector of a circle of radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 18

A runner completes one lap around a circular track of radius 50 meters. What is the total distance run?

Accepted Answer

$$100\pi$$ meters

Question 19

Convert $$2.75$$ radians to degrees. Round your answer to the nearest degree.

Accepted Answer

$$158^	ext{o}$$

Question 20

Which of the following statements about angular speed $$\omega is $$correct?

Accepted Answer

$$\omega = \frac{	heta}{t}$$, where $$	heta is in $$radians and $$t is $$time

Angles, Arc Length, and Circular Motion – Study Notes (Precalculus, Ch. 5.1)

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