Pythagorean Identity Verifier
Explore the fundamental trigonometric identity: sin²(θ) + cos²(θ) = 1. Enter an angle to verify!
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.
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