Question

How do you differentiate the following parametric equation: `x(t)=cost, y(t)=sint`?

Answer 1

`(dy)/(dx)=-cott`

Explanation:

When we deal with parametric equations like `x=x(t)` and `y=y(t)`

`(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

Here we have `x(t)=cost` hence `((dx)/(dt))=-sint`

and `y(t)=sint` hence `((dy)/(dt))=cost`

Therefore `(dy)/(dx)=cost/(-sint)=-cott`