Pythagorean Trigonometric Identity
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Full Formula Properties
Category: Trigonometry
Baby Fast Definition
No matter what angle you pick, squaring its sine and cosine and adding them always gives you 1.
This identity is the algebraic heart of the unit-circle picture: wherever you are on the circle, the sum of the squares of your coordinates is 1. It underlies every Fourier method and keeps oscillations bounded, making it indispensable in physics and engineering.
Links sine and cosine through a constant sum
Real numbers (angles) → unit circle
sin²x and cos²x always add to 1
Each term varies, but their sum never changes
Hypotenuse of a right triangle on the unit circle is always 1
The sum equals 1 for every angle x
Holds for all real x, periodic every 2π