Question

Determine $\frac{dy}{dx}$ where $x=a(1+\sin \theta )$ and $y=a(1-\cos \theta )$.

Answer 1

$x=a\left(1+\sin \theta \right)$

$y=a\left(1-\cos \theta \right)$

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

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

$\frac{dy}{dy}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}=\frac{a\sin \theta }{a\cos \theta }=\tan \theta$