Question

For \(x=a\cos^3\theta\) and \(y=a\sin^3\theta\), what are \(\frac{dx}{d\theta}\) and \(\frac{dy}{d\theta}\)?

विकल्प

• \(\frac{dx}{d\theta}=-3a\cos^2\theta\sin\theta,\ \frac{dy}{d\theta}=3a\sin^2\theta\cos\theta\)

• \(\frac{dx}{d\theta}=3a\cos^3\theta,\ \frac{dy}{d\theta}=3a\sin^3\theta\)

• \(\frac{dx}{d\theta}=3a\cos^2\theta\sin\theta,\ \frac{dy}{d\theta}=3a\sin^2\theta\cos\theta\)

• \(\frac{dx}{d\theta}=-a\sin\theta,\ \frac{dy}{d\theta}=a\cos\theta\)

Answer 1

Differentiating \(x=a\cos^3\theta\) gives \(\frac{dx}{d\theta}=-3a\cos^2\theta\sin\theta\). Differentiating \(y=a\sin^3\theta\) gives \(\frac{dy}{d\theta}=3a\sin^2\theta\cos\theta\).