# How do you find the slope of the tangent line to a polar curve?

A polar equation of the form $r = r \left(\theta\right)$ can be converted into a pair of parametric equations
$\left\{\begin{matrix}x \left(\theta\right) = r \left(\theta\right) \cos \theta \\ y \left(\theta\right) = r \left(\theta\right) \sin \theta\end{matrix}\right.$.
The slope $m$ of the tangent line at $\theta = {\theta}_{0}$ can be expressed as
$m = \frac{\mathrm{dy}}{\mathrm{dx}} {|}_{\theta = {\theta}_{0}} = \frac{\frac{\mathrm{dy}}{d \theta} {|}_{\theta = {\theta}_{0}}}{\frac{\mathrm{dx}}{d \theta} {|}_{\theta = {\theta}_{0}}} = \frac{y ' \left({\theta}_{0}\right)}{x ' \left({\theta}_{0}\right)}$.