Pythagorean Identity

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Fundamental identity relating sine and cosine

The Formula

sin²(θ) + cos²(θ) = 1

Variables & Symbols

θ

Any angle

When to Use This Formula

  • Simplifying trig expressions
  • Proving identities
  • Calculus

Worked Examples

Example 1

Problem:

If sin(θ) = 0.6, find cos(θ)

Solution: cos(θ) = ±0.8

Step-by-Step:

1

0.6² + cos²(θ) = 1

2

cos²(θ) = 1 - 0.36 = 0.64

3

cos(θ) = ±0.8

Common Mistakes to Avoid

  • Forgetting ± when taking square root
  • Sign errors

Real-World Applications

1

Signal processing

2

Physics oscillations

3

Engineering

Practice Problems

Problem 1: If cos(θ)=0.8, find sin(θ)

Show Answer

Answer: ±0.6

Related Formulas

sine definition

View Formula →

cosine definition

View Formula →

tan identity

View Formula →

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trigonometryidentitypythagorean

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