$x=a(\cos \theta+\theta\sin \theta), y=a(\sin \theta-\theta\cos\theta).$ What is $\frac{dy}{dx}$?
Answer & explanation
Correct answer: option 1
$\frac{dx}{d\theta}=a\theta\cos\theta$, $\frac{dy}{d\theta}=a\theta\sin \theta$. Hence $\frac{dy}{dx}=\frac{dy}{d\theta}/\frac{dx}{d\theta}=\tan \theta$