If x = a cos^3θ and y = a sin^3θ, then find the value of d^2y/dx^2 at θ = π/6. ​

Question

If x = a cos³θ and y = a sin³θ, then find the value of \(\frac{d^2y}{dx^2}\) at θ = \(\frac{\pi}{6}.\)

Answer 1

Given,

x = a cos³θ

Differentiating both sides with respect to θ, we get

\(\frac{dx}{d\theta}=\) - 3a cos²θ.sin θ  ...(i)

Also,

y = a sin³θ

Differentiating both sides with respect to θ, we get

\(\frac{dy}{d\theta}=\)  3a sin²θ.cos θ  ...(ii)

Now,