How to Compute the Reference Angles in Radians

By Mary Jane Sterling

Solving for the reference angle in radians is much easier than trying to determine a trig function for the original angle. To compute the measure (in radians) of the reference angle for any given angle theta, use the rules in the following table.

Finding Reference Angles in Radians
Quadrant Measure of Angle Theta Measure of Reference Angle
I 0 to π/2 è
II π/2 to π ð – è
III π to 3π/2 è – ð
IV 3π/2 to 2π 2ð – è

To find the reference angle for


  1. Determine the quadrant in which the terminal side lies.

    An angle measuring


    has its terminal side in QII, which you know because


    is slightly less than 1, making the angle slightly less than π.

  2. Do the operation indicated for that quadrant.



    from π. When you do so, you get


    so the reference angle is