for-the-parametric-curve-given-by-x2sintx2sin-t-y5costy5cos-t-find-dydxdfracdydx

Question

For the parametric curve given by x=2sin⁡tx=2\sin t, y=5cos⁡ty=5\cos t, find dydx\dfrac{dy}{dx} in terms of tt and evaluate it at t=πt=\pi.

Accepted Answer

dydx∣t=−52tan⁡t\dfrac{dy}{dx}\Big|_{t}=-\dfrac{5}{2}	an tdydx∣t=π=0\dfrac{dy}{dx}\Big|_{t=\pi}=0

Answer

dydx∣t=−52tan⁡t\dfrac{dy}{dx}\Big|_{t}=-\dfrac{5}{2}	an tdydx∣t=π is undefined\dfrac{dy}{dx}\Big|_{t=\pi}	ext{ is undefined}

Answer

dydx∣t=−25cot⁡t\dfrac{dy}{dx}\Big|_{t}=-\dfrac25\cot tdydx∣t=π is undefined\dfrac{dy}{dx}\Big|_{t=\pi}	ext{ is undefined}

Answer

dydx∣t=−25cot⁡t\dfrac{dy}{dx}\Big|_{t}=-\dfrac25\cot tdydx∣t=π=0\dfrac{dy}{dx}\Big|_{t=\pi}=0

For the parametric curve given by x=2sintx=2\(\sin\) t, y=5costy=5\(\cos\) t, find dydx\(\dfrac{dy}{dx}\) in terms of tt and evaluate it at t=πt=\(\pi\).