Question

Write the polar equation as a set of parametric equations.

r=3sinθ
Show all work.

Answer 1

`x=t`

`y=\pm√(3t-t^2)`

Explanation:

The given polar equation is;

`r=3\sin \theta`

We multiply both sides by r

`r^2=3r\sin \theta`

The corresponding rectangular equation is

`y^2+x^2=3x`

`y^2=3x-x^2`

`y=√(3x-x^2)`

Let x=t,

Then;

`y=\pm √(3t-t^2)`