Reference angle

Definition

A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. It is always between $0^{\circ}$ and $90^{\circ}$ inclusive.

5 Must Know Facts For Your Next Test

1. The reference angle is always positive.
2. For angles in the first quadrant, the reference angle is the angle itself.
3. For angles in the second quadrant, subtract the angle from $180^{\circ}$ to find the reference angle.
4. For angles in the third quadrant, subtract $180^{\circ}$ from the angle to determine the reference angle.
5. For angles in the fourth quadrant, subtract the angle from $360^{\circ}$ to get the reference angle.

Review Questions

• What is a reference angle and why is it useful?
• How do you determine the reference angle for an angle located in each of the four quadrants?
• If an angle measures $210^{\circ}$, what is its reference angle?

Related terms

Unit Circle: A circle with a radius of one centered at the origin of a coordinate plane used to define trigonometric functions.

Terminal Side: The position of an angle after it has been rotated around its vertex from its initial side.

Quadrants: $4$ regions into which a coordinate plane is divided by its x-axis and y-axis.