If x = acosθ, y = asinθ, then (dy)/(dx) at θ = π/2 will be:

If $x = a\cos\theta,\ y = a\sin\theta$, then $\dfrac{dy}{dx}$ at $\theta = \dfrac{\pi}{2}$ will be:

(a)$-1$
(b)Not defined
(c)$\dfrac{1}{a}$
(d)$0$

Answer

Correct option: (d)

Answer: (d) $0$ $\dfrac{dy}{dx} = \dfrac{dy/d\theta}{dx/d\theta} = \dfrac{a\cos\theta}{-a\sin\theta} = -\cot\theta$, which is $-\cot\dfrac{\pi}{2} = 0$ at $\theta = \dfrac{\pi}{2}$.