# How do you differentiate the following parametric equation:  (sint,tcost-pit)?

Jan 4, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{\pi + \sin t}{\cos} t$

#### Explanation:

$x \left(t\right) = \sin t$
$y \left(t\right) = \cos t - \pi t$

$x ' \left(t\right) = \cos t$
$y ' \left(t\right) = - \sin t - \pi$

The derivative of a parametric function can be found through

$\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = - \frac{\pi + \sin t}{\cos} t$