Question

If $x=\sin \theta ,y=\cos \theta$ find $\frac{dy}{dx}$

Answer 1

Consider $x=\sin \theta$

$\frac{dx}{d\theta }=\cos \theta$

$y=\cos \theta$

$\frac{dy}{d\theta }=-\sin \theta$

$\therefore \frac{dy}{dx}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}$

$=\frac{-\sin \theta }{\cos \theta }$

$=\frac{-x}{y}$

$\therefore \frac{dy}{dx}=\frac{-x}{y}$