Coterminal angles

Definition

Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. They differ by an integer multiple of $360^\circ$ or $2\pi$ radians.

5 Must Know Facts For Your Next Test

1. Coterminal angles can be found by adding or subtracting $360^\circ$ or $2\pi$ radians to/from a given angle.
2. An angle of $30^\circ$ has coterminal angles such as $390^\circ$, $-330^\circ$, etc.
3. Coterminal angles have the same sine and cosine values.
4. Any angle is coterminal with itself plus any integer multiple of $360^\circ$ or $2\pi$ radians.
5. In trigonometric functions, coterminal angles yield identical results.

Review Questions

• How do you find a coterminal angle for a given angle?
• Why do coterminal angles have the same sine and cosine values?
• What are two coterminal angles for $45^\circ$?

Related terms

Unit Circle: A circle with a radius of 1 centered at the origin of the coordinate system.

Radian: A unit of angular measure where one radian is the angle subtended by an arc equal in length to the radius of the circle.

Standard Position: An angle positioned so its vertex is at the origin and its initial side lies along the positive x-axis.