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Pythagorean Identity Calculator

Verify sin²θ + cos²θ = 1 from sine and cosine values

Pythagorean Identity Formula

sin²θ + cos²θ = 1

The Pythagorean identity connects sine and cosine for every angle. It comes from the unit circle equation x² + y² = 1, where x is cosine and y is sine.

Rounded decimal inputs may give a value very close to 1 rather than exactly 1.

How the Pythagorean Identity Works

On the unit circle, cosine and sine are coordinates of a point one unit from the origin. Squaring and adding them always gives one.

Sine Term

Square the sine value.

Cosine Term

Square the cosine value.

Add Together

The sum should equal 1.

Rounding

Decimals can create tiny differences.

💡 Example: For sin=0.6 and cos=0.8, sin²+cos²=0.36+0.64=1.

Applications of Pythagorean Identity

Identity ProofsEquation SolvingUnit CircleCalculus

Frequently Asked Questions

What is a Pythagorean identity calculator?
It checks whether sine and cosine values satisfy sin²θ + cos²θ = 1.
What is the main Pythagorean identity?
The main identity is sin²θ + cos²θ = 1.
How do I use this calculator?
Enter sine and cosine values, then click Calculate.
Why might the result not equal exactly 1?
Rounded decimal inputs can produce a small difference from 1.
Where is this identity used?
It is used in simplifying expressions, proving identities, solving equations, and calculus.

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