if x = 2cosθ and y= 6sinθ find dy/dx in term of θ  This is Parametric equation 

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to form the polar equation and then you need to convert the polar form in cartesian form.

Hence, differentiating `y = 6 sin theta`  both sides yields:

`(dy)/(dx) = (dy)/(d theta)*(d theta)/(dx)`

`(dy)/(dx) = 6 cos theta *(d theta)/(dx)`

You need to differentiate both sides `x = 2cos theta`  such that:

`dx = -2sin theta d theta`

You need to divide by `dx`  both sides such that:

`1 =-2sin theta *(d theta)/(dx)`

`(d theta)/(dx) = -1/(2sin theta)`

You need to substitute `-1/(2sin theta)`  for `(d theta)/(dx)`  in `(dy)/(dx) = 6 cos theta *(d theta)/(dx)`  such that:

`(dy)/(dx) = 6 cos theta *(-1/(2sin theta))`

`(dy)/(dx) = -3 cot theta`

Hence, evaluating `(dy)/(dx)`  in terms of theta yields `(dy)/(dx) = -3 cot theta.`