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
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.
Do the operation indicated for that quadrant.
Subtract
from π. When you do so, you get
so the reference angle is
