A reference angle is the acute angle between the terminal side and the nearest x-axis. It lets you recycle first-quadrant trig values while adjusting the sign from the quadrant — these drills ask only for that acute measure.

Steps

1. Locate the quadrant of θ.
2. QI: reference = θ; QII: 180° − θ; QIII: θ − 180°; QIV: 360° − θ.
3. Confirm the result is between 0° and 90°.