Reference Angles

Reference angles are basically reduced fractions.

Reference angles must be between 0 and 90 degrees.

In order to find the reference angle:

1. You find the original quadrant and sketch.

2. You determine whether or not the angle is positive or negative by using the unit circle.

3. You subtract either 360 degrees or 180 degrees until the value of the number is between 0 and 90.

Example 1:

Express cos240 degrees in terms of a reference angle.

In quadrant 2, which is negative when using cosine.

Subtract 180 from 240 which is 60.

Your reference angle is 60 degrees.