Question

If \(x=a\cos t\) and \(y=a\sin t\), what is \(\frac{dy}{dx}\)?

Options

• \(-\cot t\)

• \(\tan t\)

• \(-\tan t\)

• \(\cot t\)

Answer 1

Using \(\frac{dy}{dx}=\frac{dy/dt}{dx/dt}\), we obtain \(\frac{dy}{dx}=\frac{a\cos t}{-a\sin t}\). Cancelling \(a\) and simplifying gives \(\boxed{\frac{dy}{dx}=-\cot t}\).