Question

Find dy/dx any one x=acost , y=asint​

Answer 1

Answer:

$x=a \cos t \implies \dfrac{dx}{dt}=-a \sin t$

$y= a \sin t \implies \dfrac{dy}{dt}=a \cos t$

Using the chain rule:

$\begin{aligned}\implies \dfrac{dy}{dx} & =\dfrac{dy}{dt} \times \dfrac{dt}{dx}\\\\& = a \cos t \times \dfrac{1}{-a \sin t}\\\\& = \dfrac{a \cos t}{-a \sin t}\\\\& = - \dfrac{\cos t}{\sin t}\\\\& = - \cot t\end{aligned}$