三角関数の定義から，\[\begin{align}sin \theta&=y\\cos \theta&=x\\tan \theta &=\frac{y}{x}\end{align}\]となりますが，上図から，\[\begin{align}sin (-\theta)&=-y\\cos (-\theta)&=x\\tan (-\theta) &=\frac{-y}{x}\end{align}\]となります．
従って，\[\begin{align}sin(-\theta)&=-sin(\theta)\\cos(-\theta)&=cos(\theta)\\tan(-\theta)&=-tan(\theta)\end{align}\]となります．
Mathematics is the language with which God has written the universe.