Verify sin²θ + cos²θ = 1 from sine and cosine values
Result
Identity Check
Step-by-Step Derivation
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.
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