$$\frac{\text{Degrees}}{180^\circ} = \frac{\text{Radians}}{\pi}$$

$$x \times \frac{180^\circ}{\pi}$$

$$R \times \frac{180^\circ}{\pi}$$

Question 1

What is the equation of the circle shown in the images, assuming it is centered at the origin and has a radius of 1?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 2

If an angle measures $$90^\circ$$, what is its measure in radians?

Accepted Answer

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

Question 3

Which of the following best describes the relationship between degrees and radians as shown in the study materials?

Accepted Answer

$$\frac{	ext{Degrees}}{180^\circ} = \frac{	ext{Radians}}{\pi}$$

Question 4

A central angle in a unit circle subtends an arc of length $$\frac{\pi}{2}. $$What is the measure of this angle in degrees?

Accepted Answer

$$90^\circ$$

Question 5

If you walk around the entire circumference of the unit circle, how many radians have you traveled?

Accepted Answer

$$2\pi$$

Question 6

Convert $$120^\circ to $$radians using the conversion method shown in the study materials.

Accepted Answer

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

Question 7

Which of the following statements is true about the unit circle?

Accepted Answer

Every point on the circle is exactly 1 unit away from the origin.

Question 8

A sector of a unit circle has a central angle of $$\frac{\pi}{3}$$ radians. What fraction of the circle's area does this sector represent?

Accepted Answer

$$\frac{1}{6}$$

Question 9

If an angle is $$x$$ radians, what is its equivalent in degrees?

Accepted Answer

$$x 	imes \frac{180^\circ}{\pi}$$

Question 10

A Ferris wheel makes one complete revolution. What is the angle in radians that the wheel has rotated?

Accepted Answer

$$2\pi$$

Question 11

Which of the following is the correct formula for converting $$R$$ radians to degrees?

Accepted Answer

$$R 	imes \frac{180^\circ}{\pi}$$

Question 12

A clock's minute hand moves from 12 to 3. What is the angle in radians that the hand has swept?

Accepted Answer

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

Question 13

If the radius of a circle is doubled, what happens to the equation of the circle centered at the origin?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 14

A sector of a circle with radius 1 has an area of $$\frac{\pi}{4}. $$What is the measure of the central angle in radians?

Accepted Answer

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

Question 15

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

Accepted Answer

$$390^\circ$$

The Unit Circle and Angle Measurement in Precalculus

Study Guide - Practice Questions