Math
Pythagorean identities.
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
Real-world.
- 1 If sin θ = 3/5, then cos²θ = 1 − 9/25 = 16/25, so cos θ = ±4/5
- 2 Simplifying sin²x + cos²x in an expression by replacing it with 1
Key Fact
sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ