I chose to do this because the new unit just started, and I need to reinforce these ideas.

Rotation angles describe the measure of an angle formed by rotating a line from its initial position (usually along the positive x-axis) to its terminal position.

Reference angles are the smallest angles that a given angle makes with the x-axis. They are always measured as positive acute angles (between 0° and 90°). To find a reference angle, you typically subtract the given angle from the nearest multiple of 180° or 360°, depending on the quadrant in which the terminal side of the angle lies.

You can determine the reference angle from the rotation angle, and you can determine the rotation angle from the reference angle.

Rotation: 135°

We can see that the terminal arm is in quadrant II, meaning the closest reference is 180°. Subtract 135° from 180° and you get a reference angle of 45°.

Reference: 60°

The reference angle is in quadrant IV, so the closest reference is 360°. Subtract 60° from 360° and you’re left with 300°.