How to Compute the Reference Angles in Radians - dummies

# How to Compute the Reference Angles in Radians

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.

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.

Subtract

from π. When you do so, you get

so the reference angle is