Reference angles

Math

Definition

The acute angle formed between the terminal side of an angle and the x-axis. Reference angles help find trigonometric values for any angle by relating them back to first-quadrant values.

Examples

  • The reference angle for 150° is 180° - 150° = 30°
  • The reference angle for 225° is 225° - 180° = 45°
  • The reference angle for 300° is 360° - 300° = 60°
Key Fact

QI: ref = θ; QII: ref = 180° - θ; QIII: ref = θ - 180°; QIV: ref = 360° - θ

Related Terms

Unit circle Trig values of any angle Coterminal angles Quadrants

Study This Concept

Practice reference angles with free review games in these units:

Trigonometry Unit 3: Unit Circle