Q: A Ferris wheel with a radius of $$10$$ meters makes one complete revolution every $$30$$ seconds. What is the linear speed of a seat on the Ferris wheel?

$$\frac{2\pi \times 10}{30} m/s$$

Q: A car tire has a radius of $$0.3$$ meters and rotates at $$120$$ revolutions per minute. What is the linear speed of a point on the edge of the tire in meters per second?

$$0.3 \times 2\pi \times 2 m/s$$

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 $$42^	ext{o} 18' 36'' to $$decimal degrees. Round your answer to four decimal places.

Accepted Answer

$$42.3100^	ext{o}$$

Question 3

A central angle of $$2$$ radians in a circle of radius $$5$$ meters subtends an arc. What is the length of the arc?

Accepted Answer

$$10$$ meters

Question 4

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

Accepted Answer

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

Question 5

Convert $$-\frac{\pi}{4}$$ radians to degrees.

Accepted Answer

$$-45^	ext{o}$$

Question 6

A circle has a radius of $$8 cm. $$What is the area of a sector formed by a central angle of $$60^	ext{o}$$? (Round to two decimal places.)

Accepted Answer

$$33.51 cm$^2$$

Question 7

A Ferris wheel with a radius of $$10$$ meters makes one complete revolution every $$30$$ seconds. What is the linear speed of a seat on the Ferris wheel?

Accepted Answer

$$\frac{2\pi 	imes 10}{30} m/s$$

Question 8

If the latitude of City A is $$40^	ext{o} N $$and City B is $$50^	ext{o} N$$, and both are due north-south of each other, what is the central angle between them in radians?

Accepted Answer

$$\frac{10\pi}{180}$$

Question 9

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

Accepted Answer

$$6\pi$$ radians/second

Question 10

Which of the following is true about a quadrantal angle?

Accepted Answer

Its terminal side lies on the x-axis or y-axis.

Question 11

Find the area of a sector of a circle with radius $$6$$ meters and central angle $$\frac{\pi}{3}$$ radians.

Accepted Answer

$$6\pi m$^2$$

Question 12

A car tire has a radius of $$0.3$$ meters and rotates at $$120$$ revolutions per minute. What is the linear speed of a point on the edge of the tire in meters per second?

Accepted Answer

$$0.3 	imes 2\pi 	imes 2 m/s$$

Question 13

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 14

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

Accepted Answer

$$143^	ext{o}$$

Question 15

A sector of a circle has an area of $$10 m$^2$$ and a radius of $$4 m. $$What is the measure of the central angle in radians?

Accepted Answer

$$1.25$$ radians

Chapter 5: Trigonometric Functions – Angles, Arc Length, and Circular Motion

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