# How do you differentiate the following parametric equation:  x(t)=cost, y(t)=sint ?

Sep 10, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \cot t$

#### Explanation:

When we deal with parametric equations like $x = x \left(t\right)$ and $y = y \left(t\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$

Here we have $x \left(t\right) = \cos t$ hence $\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right) = - \sin t$

and $y \left(t\right) = \sin t$ hence $\left(\frac{\mathrm{dy}}{\mathrm{dt}}\right) = \cos t$

Therefore $\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \frac{t}{- \sin t} = - \cot t$