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

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

Question 1

Which formula correctly converts an angle from degrees to radians?

Accepted Answer

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

Question 2

A medical imaging device rotates $$540^\circ to $$scan a patient. What is this angle in radians?

Accepted Answer

$$6\pi/1$$

Question 3

A wind turbine blade rotates $$2\pi$$ radians. How many degrees has it rotated?

Accepted Answer

$$360^\circ$$

Question 4

If a car's steering wheel turns $$-\dfrac{7\pi}{6}$$ radians, what is the equivalent angle in degrees?

Accepted Answer

$$-210^\circ$$

Question 5

Which of the following is the correct conversion for $$120^\circ to $$radians?

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 6

A satellite completes a rotation of $$\dfrac{5\pi}{4}$$ radians. What is this angle in degrees?

Accepted Answer

$$225^\circ$$

Question 7

Which of the following angles is equivalent to $$270^\circ in $$radians?

Accepted Answer

$$\dfrac{3\pi}{2}$$

Question 8

A clock's minute hand moves $$\dfrac{\pi}{2}$$ radians. How many degrees has it moved?

Accepted Answer

$$90^\circ$$

Question 9

If a gymnast spins $$315^\circ$$, what is the angle in radians?

Accepted Answer

$$\dfrac{7\pi}{4}$$

Question 10

A rotating machine part turns $$-\dfrac{\pi}{3}$$ radians. What is the equivalent angle in degrees?

Accepted Answer

$$-60^\circ$$

Question 11

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

Accepted Answer

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

Question 12

A Ferris wheel rotates $$\dfrac{3\pi}{2}$$ radians. How many degrees is this?

Accepted Answer

$$270^\circ$$

Question 13

A pizza is sliced into 8 equal pieces. What is the angle in radians of each slice?

Accepted Answer

$$\dfrac{\pi}{4}$$

Question 14

A radar antenna rotates $$150^\circ. $$What is the angle in radians?

Accepted Answer

$$\dfrac{5\pi}{6}$$

Question 15

A wheel turns $$\dfrac{11\pi}{6}$$ radians. What is the equivalent angle in degrees?

Accepted Answer

$$330^\circ$$

Radians: Converting Between Degrees and Radians

Study Guide - Practice Questions