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Degree to Radian Measure

The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.  In radians, one complete counterclockwise revolution is 2 π and in degrees, one complete counterclockwise revolution is 360 ° .  So, degree measure and radian measure are related by the equations
360 ° = 2 π  radians

and

180 ° = π  radians

From the latter, we obtain the equation 1 ° = π 180  radians .  This leads us to the rule to convert degree measure to radian measure.  To convert from degrees to radians, multiply the degrees by π 180 °  radians .

Example 1:

Convert 60 ° to radian measure.

( 60 ° ) ( π 180 °  rad ) = π 3  rad

Example 2:

Convert 150 ° to radian measure.

( 150 ° ) ( π 180 °  rad ) = 5 π 6  rad