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 angle.

A angle and a angle are coterminal with a angle.