Reference angles are like reduced fractions. Reference angles are used to find trig functions by using degrees between 0 and 90 degrees, because you can use a trig chart for angles between 0 and 90 degrees. To find a reference angle, first sketch the angle and decide which quadrant it is in. If the angle is negative, you go that many degrees counterclockwise. Then determine if it is positive or negative by checking the unit circle. To finish, subtract or add 180 degrees until you have an angle between 0 and 90.

Example: Find the reference angle.

1. Tan 225 degrees

Tangent is y/x. 225 degrees is in Quadrant 3. Y is negative in Quadrant 3. X is also negative in Quadrant 3. So a negative over a negative equals a positive. 225-180=45. Tan225 degrees = tan 45 degrees.

2. Cos 120 degrees

Cosine is x/r. 120 degrees is in Quadrant 2. X is negative in Quadrant 2. 120-180=60. Cos 120 degrees = -Cos 60 degrees.

3. Sin 330 degrees

Sine is y/r. 330 degrees is in Quadrant 4. Y is negative in Quadrant 4. 330-180=150. 150-180=30. Sin 330 degrees = -Sin 30 degrees.