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Question

If $$x=3\sin {t} ,\ y=3\cos {t} ,$$ then find $$\dfrac {dy}{dx}$$ at $$t=\dfrac { \pi  }{ 3 } $$.


Solution

$$x=3\sin t$$
Differentiating w.r.t. t, we get,
$$\dfrac{dx}{dt}=3\cos t$$

$$y=3\cos t$$
Differentiating w.r.t. t, we get,
$$\dfrac{dy}{dt}=-3\sin t$$

Thus, $$\dfrac{dy}{dx}=-\tan t$$

At $$t=\dfrac{\pi}{3}$$,
$$\dfrac{dy}{dx}=-\sqrt3$$

Mathematics

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