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Radian to Degree 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 radian = ( 180 π ) o .  This leads us to the rule to convert radian measure to degree measure.  To convert from radians to degrees, multiply the radians by 180 ° π radians .

Example 1:

Convert π 4 radians to degrees.

( π 4 rad ) ( 180 ° π rad ) = ( 180 4 ) o = 45 °

Example 2:

Convert 9 π 5 radians to degrees.

( 9 π 5 rad ) ( 180 ° π rad ) = 9 ( 36 ) o = 324 °

Example 3:

Convert 3 radians to degrees.

( 3 rad ) ( 180 ° π rad ) = ( 540 π ) o 171.89 °