Sum of Squares of Sine and Cosine/Proof 2

Theorem

 * $\cos^2 x + \sin^2 x = 1$

where $\sin$ and $\cos$ are sine and cosine.

Geometric Proof

 * Starting with $\sin x$ and $\cos x$:


 * $\displaystyle \sin x = \dfrac{\text{opposite}}{\text{hypotenuse}}$


 * $\displaystyle \cos x = \dfrac{\text{adjacent}}{\text{hypotenuse}}$


 * Squaring both sides and adding them together gives:


 * $\displaystyle \sin^2 x + \cos^2 x = \frac{\text{opposite}^2 + \text{adjacent}^2}{\text{hypotenuse}^2} = 1$ by Pythagoras's Theorem