Question

Write the polar equation as a set of parametric equations. r=3sinθ Show all work.

Answer 1

Answer:

$x=t$

$y=\pm\sqrt{3t-t^2}$

Step-by-step 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

$y^2+x^2=3x$

$y^2=3x-x^2$

$y=\sqrt{3x-x^2}$

Let x=t,

Then;

$y=\pm \sqrt{3t-t^2}$