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

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

Question 1

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

Accepted Answer

An angle measured counterclockwise from the positive x-axis.

Question 2

What is the degree measure of one complete revolution around a circle?

Accepted Answer

$$360^\circ$$

Question 3

Which of the following angles is coterminal with $$45^\circ$$?

Accepted Answer

$$405^\circ$$

Question 4

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

Accepted Answer

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

Question 5

An angle measures $$-135^\circ. $$Which quadrant does its terminal side lie in?

Accepted Answer

Quadrant IV

Question 6

What is the radian measure of an angle whose intercepted arc is equal to the radius of the circle?

Accepted Answer

$$1$$ radian

Question 7

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

Accepted Answer

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

Question 8

Find the least non-negative coterminal angle for $$-75^\circ.$$

Accepted Answer

$$285^\circ$$

Question 9

Which of the following angles is coterminal with $$\frac{\pi}{4}$$?

Accepted Answer

$$\frac{9\pi}{4}$$

Question 10

Convert $$-\frac{3\pi}{2}$$ radians to degrees.

Accepted Answer

$$-270^\circ$$

Question 11

A clock’s minute hand moves from 12 to 3. What is the angle in radians swept by the hand?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

If an angle in standard position has its terminal side on the negative y-axis, what is its degree measure?

Accepted Answer

$$270^\circ$$

Question 14

Which of the following is a coterminal angle with $$-\frac{5\pi}{3}$$?

Accepted Answer

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

Question 15

A sector of a circle has a central angle of $$60^\circ$$ and a radius of 10 cm. What is the length of the intercepted arc?

Accepted Answer

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

Question 16

Which of the following angles is in Quadrant II?

Accepted Answer

$$120^\circ$$

Question 17

Find the least non-negative coterminal angle for $$-\frac{7\pi}{6}.$$

Accepted Answer

$$\frac{5\pi}{6}$$

Question 18

If an angle is measured as $$-240^\circ$$, what is its least positive coterminal angle?

Accepted Answer

$$120^\circ$$

Question 19

Which of the following is the radian measure for $$270^\circ$$?

Accepted Answer

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

Question 20

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

Accepted Answer

$$2$$ radians

Angles: Degree and Radian Measure in Precalculus

Study Guide - Practice Questions