Find a Reference Angle

7- 4 Finding a Reference Angle

Follow these steps to find a reference angle:
1. Locate which quadrant the angle is in.
2. Decide whether it is positive or negative.
3. Subtract 180 until the absolute value of theta is between 0 and 90 degrees.
4. If your answer is a trig chart angle plug it in. If it’s not you leave it alone or you plug it into your calculator.

Trig Chart Angles:
0 degrees = 0
30 degrees = pi/6
45 degrees = pi/4
60 degrees = pi/3
90 degrees = pi/2

Here are some examples you can try:

Find the reference angles:

Example 1:

sin(690°) = -sin(30°) = -π/6

690° is in the IV quadrant. They are asking for sin, and in the IV quadrant sin is negative. So we subtract 180° continuously from 690°, until we arrive at 30°. We then plug 30° into –sin and get-π/6, our answer.

Example 2:

cos(400°)=cos(40°)

400° is in quadrant I, which for cos is positive. We continuously subtract 180° from 400°, until we get an angle between 0° and 90°, which is 40°. Our final answer is cos(40°).