The fundamental identity

Property — Fundamental identity

For every $\alpha\in\mathbb{R}$: $\sin^2\alpha + \cos^2\alpha = 1.$ It is simply the equation of the unit circle $x^2+y^2=1$ evaluated at $P_\alpha$: since $\cos\alpha$ and $\sin\alpha$ are the abscissa and ordinate of a point of the circle, the sum of their squares equals $1$.

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Topics: Trigonometry
Concepts: Cosine · Fundamental identity · Sine
Functions: Cosine · Sine
Skills: Proving