Pythagorean identities

Math

Definition

Three fundamental trigonometric identities derived from the Pythagorean theorem and the unit circle. They express relationships between sin, cos, tan, cot, sec, and csc that are true for all angles where the functions are defined.

Examples

  • If sin θ = 3/5, then cos²θ = 1 − 9/25 = 16/25, so cos θ = ±4/5
  • Simplifying sin²x + cos²x in an expression by replacing it with 1
Key Fact

sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ

Related Terms

Unit circle Verifying identities Sine cosine tangent Double-angle formulas

Study This Concept

Practice Pythagorean identities with free review games in these units:

Trigonometry Unit 5: Trigonometric Identities