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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.

Math diagram

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 2 π 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.

    Math diagram

Example 2:

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

π 3 + 2 π = 7 π 3 π 3 2 π = 5 π 3

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

    Math diagram

 

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