Q: Which of the following is the correct formula to convert radians to degrees?

Degrees $$= \text{Radians} \times \frac{180}{\pi}$$

Q: Which of the following is the correct relationship for finding a coterminal angle in radians?

$$\theta + 2\pi k$$, where $$k is an $$integer

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 lies along the positive x-axis.

Question 2

A central angle in a circle of radius $$r$$ intercepts an arc of length $$s. $$What is the radian measure $$	heta of $$the angle?

Accepted Answer

$$	heta = \frac{s}{r}$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following angles is a quadrantal angle?

Accepted Answer

$$270^\circ$$

Question 5

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

Accepted Answer

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

Question 6

If an angle measures $$-210^\circ$$, what is a positive coterminal angle less than $$360^\circ$$?

Accepted Answer

$$150^\circ$$

Question 7

A wheel rotates at an angular speed of $$12$$ radians per second. If the radius of the wheel is $$0.5$$ meters, what is the linear speed at the rim?

Accepted Answer

$$6$$ meters per second

Question 8

Which of the following is the correct formula to convert radians to degrees?

Accepted Answer

Degrees $$= 	ext{Radians} 	imes \frac{180}{\pi}$$

Question 9

A central angle of $$2$$ radians in a circle intercepts an arc of $$8 cm. $$What is the radius of the circle?

Accepted Answer

$$4 cm$$

Question 10

A 45-rpm record has a radius of $$3$$ inches. What is the linear speed at the edge of the record in inches per minute? (1 revolution = $$2\pi$$ radians)

Accepted Answer

$$270\pi$$ inches/min

Question 11

Which of the following statements about coterminal angles is true?

Accepted Answer

Coterminal angles have the same initial and terminal sides but may have different measures.

Question 12

If a point moves along a circle of radius $$5$$ meters and sweeps out an angle of $$\frac{\pi}{2}$$ radians in $$4$$ seconds, what is its angular speed?

Accepted Answer

$$\frac{\pi}{8}$$ radians/second

Question 13

Which of the following angles is NOT coterminal with $$30^\circ$$?

Accepted Answer

$$120^\circ$$

Question 14

A central angle of $$\frac{3\pi}{4}$$ radians intercepts an arc of $$15 cm. $$What is the radius of the circle?

Accepted Answer

$$20 cm$$

Question 15

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

Accepted Answer

It is generated by a clockwise rotation from the initial side.

Question 16

If a car tire with a radius of $$0.4$$ meters rotates through $$5$$ revolutions, what is the total distance traveled by a point on the edge of the tire?

Accepted Answer

$$4\pi$$ meters

Question 17

Convert $$\frac{7\pi}{6}$$ radians to degrees.

Accepted Answer

$$210^\circ$$

Question 18

A central angle of $$60^\circ$$ intercepts an arc of $$8 cm. $$What is the radius of the circle?

Accepted Answer

$$\frac{24}{\pi} cm$$

Question 19

Which of the following is the correct relationship for finding a coterminal angle in radians?

Accepted Answer

$$	heta + 2\pi k$$, where $$k is an $$integer

Question 20

A Ferris wheel rotates at $$0.2$$ radians per second. If the radius is $$10$$ meters, what is the linear speed of a seat on the rim?

Accepted Answer

$$2$$ meters/second

Angles and Radian Measure: Foundations of Trigonometry

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