A mathematical detour

Pythagoras and trigonometry

[triangle] \[ \begin{eqnarray*} \sin\theta & = & \dfrac{a}{c} \\ \cos\theta & = & \dfrac{b}{c} \\ \tan\theta & = & \dfrac{a}{b} \\ \tan\theta & = & \dfrac{\sin\theta}{\cos\theta} \end{eqnarray*} \]