Question:
Find $\frac{d y}{d x}$, when
$x=a \cos \theta$ and $y=b \sin \theta$
Solution:
We have, $x=a \cos \theta$ and $y=b \sin \theta \Rightarrow \frac{d x}{d \theta}=-a \sin \theta$ and $\frac{d y}{d \theta}=b \cos \theta \therefore \frac{d y}{d x}=\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}}=\frac{b \cos \theta}{-a \sin \theta}=-\frac{b}{a} \cot \theta$
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