Reference Angles

Definition: A reference angle is an angle formed between the terminal side (far side) of an angle and the closest side of the x-axis. Reference angles are always between 0° and 90°.

refangle2.pngExample: Find the reference angle for -160°.

Solution:

Step 1: Figure out where this angle is. You can either draw it out or think about it. -160° means that we are going clockwise 160° to quadrant III.

Step 2: Figure out how far the opening of the angle is from the x-axis. Since the x-axis is at 180 or -180 degrees, we know that we are 20 degrees away.

-180° – (-160°) = 20°

This tells us the reference angle is 20°.

ref angle.png

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