Question

How do you graph `r = 4sin(theta)`?

Answer 1

The graph belongs to the conic family called circle. Assign several values for `theta` then compute corresponding `r` then plot the graph

Explanation:

The given `r=4sin theta` is equivalent to

`x^2+y^2=4y`

and by completing the square

`x^2+y^2-4y+4-4=0`
`(x-0)^2+(y-2)^2=4`

also using the "center-radius form#

`(x-h)^2+(y-k)^2=r^2`
`(x-0)^2+(y-2)^2=2^2`
center `(h, k)=(0, 2)`

with radius `r=2`

now, you are ready to graph

kindly see the graph below
graph{x^2+y^2=4y[-10,10,-5,5]}

You may also use `r=4 sin theta` right away by assigning values for `theta` and noting all `(r, theta)` coordinates.

God bless you...