What is the derivative of f(t) = (t-sint , cost ) ?

Dec 30, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = \sin \frac{t}{\cos t - 1}$

Explanation:

$x ' \left(t\right) = 1 - \cos t$
$y ' \left(t\right) = - \sin t$

The derivative of the parametric function is

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = \frac{- \sin t}{1 - \cos t} = \sin \frac{t}{\cos t - 1}$