Question

Find $\frac{dy}{dx}$, when

$x=a\cos \mathrm{\theta }\mathrm{and}y=b\sin \mathrm{\theta }$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},x=a\cos \theta \mathrm{and}y=b\sin \theta \\ \Rightarrow \frac{dx}{d\theta }=-a\sin \theta \mathrm{and}\frac{dy}{d\theta }=b\cos \theta \\ \therefore \frac{dy}{dx}=\frac{{\displaystyle \frac{dy}{d\theta }}}{{\displaystyle \frac{dx}{d\theta }}}=\frac{b\cos \theta }{-a\sin \theta }=-\frac{b}{a}\cot \theta \end{gathered}$$