Pythagorean Identity
A point (cos θ, sin θ) lies on the unit circle, so its coordinates satisfy x² + y² = 1.
Variables
- θ — An angle in degrees or radians
When to use it
Simplifying trig expressions, converting between sine and cosine, and checking values.
Worked example
sin θ = 3/5, acute
- cos²θ = 1 − 9/25 = 16/25
- cos θ = 4/5
Answer: 4/5
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Example problems
Common mistakes
Writing sin θ²
The square is on the function: (sin θ)², often written sin²θ.
Related formulas
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Frequently asked questions
Are there other Pythagorean identities?
Yes, including 1 + tan²θ = sec²θ, obtained by dividing by cos²θ.