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Trigonometry

Pythagorean Trigonometric Identities

Formula
sin²θ + cos²θ = 1

What is Pythagorean Trigonometric Identities?

The fundamental Pythagorean identity states that the sum of the squares of sine and cosine of any angle equals 1. From this, two other identities follow: 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ.

Variables

  • θ
    θ — Any angle
  • s
    sin — Sine function
  • c
    cos — Cosine function

Worked Examples

Example 1

If sin θ = 3/5, find cos θ.

Solution:

cos²θ = 1 − sin²θ = 1 − 9/25 = 16/25. cos θ = 4/5

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