Question

How do you graph `r = 6 sin theta`?

Answer 1

In Cartesian plane draw a circle with center at `(0,3)` and radius `3`.

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is `x=rcostheta`, `y=rsintheta` and `r^2=x^2+y^2`.

We can use this to convert equation in polar coordinates to an equation with Cartesian coordinates.

`r=6sintheta`

`hArrr^2=6rsintheta`

or `x^2+y^2=6y`

or `(x-0)^2+(y^2-6y+9)=9`

or `(x-0)^2+(y-3)^2=9`

This is the equation of a circle with center at `(0,3)` and radius `3` and hence one can draw it accordingly.
graph{x^2+y^2-6y=0 [-10.42, 9.58, -2.24, 7.76]}