Verified answer

trig identity is right. You may not be able to convert the function of ø to a function of x, but you can certainly convert it into a parametric function of t.

Taking t = ø, say the following:

x = r*cos(t/3)

y = r*sin(t/3)

substituting r with its function, you have:

x = sin^3(t/3)*cos(t)

y = sin^3(t/3)*sin(t)

That graph (taking the x and y coordinates to be separate functions of t) will give you the exact same picture.