Question

$x=3cos\Theta ,y=3sin\Theta ,then\frac{dy}{dx}=?$

• A. -$cot\Theta$
• B. -$sin\Theta$
• C. $sin\Theta$
• D. $tan\Theta$

Answer 1

The correct option is A -$cot\Theta$

$x=3\cos \theta \left(\text{Given}\right)$

Differentiating w.r.t. $\theta$, we have

$\frac{dx}{d\theta }=3(-\sin \theta )=-3\sin \theta$

$\Rightarrow \frac{d\theta }{dx}=\frac{1}{-3\sin \theta }$

Similarly,

$y=3\sin \theta \left(\text{Given}\right)$

Differentiating w.r.t. $\theta$, we have

$\frac{dy}{d\theta }=3\left(\cos \theta \right)=3\cos \theta$

Now,

$\frac{dy}{dx}=\frac{dy}{d\theta }\times \frac{d\theta }{dx}$

$\Rightarrow \frac{dy}{dx}=3\cos \theta \times \frac{1}{-3\sin \theta }$

$\Rightarrow \frac{dy}{dx}=-\cot \theta$

Hence the correct answer is $\left(A\right)-\cot \theta$.