Finding Reference Angles

Trigonometry · Axiom Academy

EXAMPLE Finding Reference Angles Learn to identify quadrants and calculate reference angles for positive and negative angle measures. A reference angle is the acute angle (between 0° and 90°) formed between the terminal side of an angle and the x-axis. It's always positive! Excellent work! You've mastered finding reference angles. Here's what to remember: Reference angles are always acute: They range from 0° to 90° and are always positive Quadrant determines the formula: QI: reference angle = angle itself QII: reference angle = 180° - angle QIII: reference angle = angle - 180° QIV: reference angle = 360° - angle Handle negative angles first: Add 360° to find a positive coterminal angle, then proceed normally Coterminal angles share reference angles: -150° and 210° have the same reference angle because they're coterminal Reference angles are fundamental for evaluating trigonometric functions at any angle. Once you know the reference angle, you can find exact values using the unit circle!

This is the written version of the interactive lesson above. See the full Trigonometry course.