Find d y d x , if x = a cos , y = a sin . - Vidyadip

Question

Find $\frac{d y}{d x}$, if x = a cos $\theta$, y = a sin $\theta$.

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Answer

Given that
x = a cos $\theta$, y = a sin $\theta$
Therefore $\frac{d x}{d \theta}=-a \sin \theta, \frac{d y}{d \theta}=a \cos \theta$
Hence, $\frac{d y}{d x} $ = $\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}}=\frac{a \cos \theta}{-a \sin \theta}=-\cot \theta$

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