Q: Which of the following is the correct relationship for converting degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Question 1

Which of the following best describes a coterminal angle to $$120^\circ$$?

Accepted Answer

$$-240^\circ$$

Question 2

What is the radian measure of a straight angle?

Accepted Answer

$$\pi$$

Question 3

An angle in standard position has its terminal side on the negative y-axis. What is the degree measure of this angle?

Accepted Answer

$$270^\circ$$

Question 4

Convert $$225^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{4}$$

Question 5

A central angle in a circle of radius $$10 cm $$intercepts an arc of length $$15 cm. $$What is the radian measure of the angle?

Accepted Answer

$$1.5$$

Question 6

Which of the following angles is an obtuse angle?

Accepted Answer

$$120^\circ$$

Question 7

If an angle measures $$-90^\circ$$, in which direction was the rotation made from the initial side?

Accepted Answer

Clockwise

Question 8

A circle has a radius of $$8$$ meters. What is the length of the arc intercepted by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

$$\frac{8\pi}{3}$$ meters

Question 9

Which of the following statements is TRUE about radian measure?

Accepted Answer

It is the ratio of arc length to radius and is unitless.

Question 10

A Ferris wheel makes one complete revolution. What is the radian measure of the angle swept out by a spoke of the wheel?

Accepted Answer

$$2\pi$$

Question 11

Which of the following is the correct formula for the length $$s of an $$arc intercepted by a central angle $$\alpha (in $$radians) in a circle of radius $$r$$?

Accepted Answer

$$s = r\alpha$$

Question 12

Which of the following angles is coterminal with $$30^\circ$$?

Accepted Answer

$$390^\circ$$

Question 13

A central angle in a circle of radius $$5$$ meters intercepts an arc of length $$10\pi$$ meters. What is the degree measure of the angle?

Accepted Answer

$$360^\circ$$

Question 14

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

Accepted Answer

$$210^\circ$$

Question 15

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies on an axis

Question 16

A central angle of $$60^\circ in a $$circle of radius $$12 cm $$intercepts an arc. What is the length of the arc?

Accepted Answer

$$4\pi cm$$

Question 17

If an angle in standard position has a negative measure, what does this indicate about its rotation?

Accepted Answer

The rotation is clockwise from the initial side.

Question 18

Which of the following is the correct relationship for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Question 19

A central angle of $$\frac{\pi}{2}$$ radians in a circle of radius $$6$$ meters intercepts an arc. What is the length of the arc?

Accepted Answer

$$3\pi$$ meters

Question 20

Which of the following angles is an acute angle?

Accepted Answer

$$45^\circ$$

Angles and Their Measurements: Degree and Radian Measure

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