A) find a cartesian equation for the curve described by the given polar equation. r =3 sin g

Recall that r^2 = x^2 + y^2, so that r = sqrt(x^2+y^2).

                                                                        y
r = 3 sin g becomes    sqrt(x^2+y^2) = 3*
                                                                  sqrt(x^2+y^2)

Squaring both sides,

                    9y^2
x^2+y^2 =
                  x^2 + y^2

If this is correct (and I'm not convinced that it is), then (x^2+y^2)^2 = 9y^2
shows the relationship between x and y.  Can anyone improve on this result?