Question

If $x$ = $a$( $\sin t$) and $y$ = $a\left(\cos t\right)$ , then $\frac{dy}{dx}$ =

Answer 1

$x=a\sin t\Rightarrow \frac{dx}{dt}=a\frac{d}{dt}\left(\sin t\right)=a\cos t$

$y=a\cos t\Rightarrow \frac{dy}{dt}=a\frac{d}{dt}\left(\cos t\right)=-a\sin t$

$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{-a\sin t}{a\cos t}=-\tan t$