Question

Solve $x=a(\theta -\sin \theta ),y=a(1+\cos \theta )$ find $\frac{dy}{dx}$ ?

Answer 1

$\because x=a(\theta -\sin \theta )\Rightarrow \frac{dx}{d\theta }=a(1-\cos \theta )and,y=a(1+\cos \theta )\Rightarrow \frac{dy}{d\theta }=-a\sin \theta \because \frac{dy}{dx}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}=\frac{-a\sin \theta }{a(1-\cos \theta )}=\frac{\sin \theta }{(\cos \theta -1)}$