Question

For \(x=a\cos^3\theta\) and \(y=a\sin^3\theta\), what is \(\frac{dy}{dx}\) in terms of \(\theta\)?

Options

• \(-\cot\theta\)

• \(\cot\theta\)

• \(\tan\theta\)

• \(-\tan\theta\)

Answer 1

Using the parametric formula, \(\frac{dy}{dx}=\frac{3a\sin^2\theta\cos\theta}{-3a\cos^2\theta\sin\theta}\). Simplifying gives \(\frac{dy}{dx}=-\tan\theta\).