Question

How do you graph the polar equation `r=-3sintheta`?

Answer 1

please show the graph below

Explanation:

As `r=-3sintheta` ,at `theta=0,pi/4,pi/2,(3pi)/4 and pi`

`r` takes values `r=0,(-3)/sqrt2,-3,(-3)/sqrt2,0`

Thus these represents points `(0,0),((-3)/sqrt2,pi/4),(-3,pi/2),((-3)/sqrt2,3pi/4),(0,pi)`

We can select more such points, say by having`theta=pi/6,pi/3,(2pi)/3, (5pi)/6`

the graph will be appear as follow:

it is a circle with center `(-3/2,-pi/2)` and radius `r=3`

as `r=-3sintheta` it means `r^2=-3rsintheta`

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