Question

If \(x=a\cos t\) and \(y=a\sin t\), what are the derivatives with respect to \(t\)?

Options

• \(\frac{dx}{dt}=-a\sin t,\ \frac{dy}{dt}=a\cos t\)

• \(\frac{dx}{dt}=a\cos t,\ \frac{dy}{dt}=a\sin t\)

• \(\frac{dx}{dt}=-a\cos t,\ \frac{dy}{dt}=-a\sin t\)

• \(\frac{dx}{dt}=a\sin t,\ \frac{dy}{dt}=-a\cos t\)

Answer 1

Differentiating \(x=a\cos t\) gives \(\frac{dx}{dt}=-a\sin t\). Differentiating \(y=a\sin t\) gives \(\frac{dy}{dt}=a\cos t\).