Reference Angles

Reference angles are like reduced fractions. They are always between 0 and 90 degrees. To find a reference angle, first sketch the angle and determine the quadrant (if the angle is positive, you go that many degrees clockwise, and vice versa). Then determine if it is positive or negative by consulting the unit circle. Finally, subtract or add 180 degrees until you have an angle between 0 and 90.
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Examples:
Find a reference angle for sin280.
Sketch the graph. 280 is in the fourth quadrant and sin is y/r so it's negative.
Subtract 360 and you get 80. So the answer is -sin80 degrees.