sin² + cos² = 1

Depends on: Definition of sin / cos / tan, Pythagorean theorem.

Statement

Let $\theta$ be an acute angle in a right $\triangle ABC$ ( $\angle C = 90^\circ$ ); by Definition of sin / cos / tan,

\sin\theta \;=\; \frac{\text{opposite}}{\text{hypotenuse}},\qquad \cos\theta \;=\; \frac{\text{adjacent}}{\text{hypotenuse}}.

Then

\sin^{2}\theta + \cos^{2}\theta \;=\; 1.

$Right \triangle ABC with unit hypotenuse (\angle C = 90^\circ, |AB|=1): the two legs have lengths \sin\theta and \cos\theta; the identity \sin^2\theta+\cos^2\theta=1.$

Statement

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