Pythagorean Identity Verifier
Verify the Pythagorean identity (sin²θ + cos²θ = 1) effortlessly for any angle in degrees or radians. This online tool provides instant verification and visual representation.
Enter an angle and select the unit to verify the Pythagorean Identity.
Verification Result
The Pythagorean Identity, sin²(θ) + cos²(θ) = 1, is
Visual Representation on Unit Circle
Visual representation of the angle on the unit circle.
Understanding Pythagorean Identity
The Pythagorean Identity, sin²(θ) + cos²(θ) = 1, is a fundamental concept in trigonometry derived from the Pythagorean theorem. In a unit circle, for any angle θ, if we consider a point on the circle, the x-coordinate is cos(θ) and the y-coordinate is sin(θ). Applying the Pythagorean theorem (a² + b² = c²) to the right-angled triangle formed by this point, the origin, and the x-axis projection, we get cos²(θ) + sin²(θ) = 1², which simplifies to sin²(θ) + cos²(θ) = 1.
This identity holds true for all real values of θ and is crucial in simplifying trigonometric expressions and solving equations. It highlights the relationship between sine and cosine functions and their geometric interpretation on the unit circle.