Coterminal Angles

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.  For example 30° , 330° and 390° are all coterminal.

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians.

Example 1:

Find a positive and a negative angle coterminal with a 55° angle.

55°360°=305° 55°+360°=415°

A 305° angle and a 415° angle are coterminal with a 55° angle.

              

Example 2:

Find a positive and a negative angle coterminal with a π 3 angle.

π 3 +2π= 7π 3 π 3 2π= 5π 3

A 7π 3 angle and a 5π 3 angle are coterminal with a π 3 angle.