How do you convert a polar equation where there is a number in front of theta (sinus or cosinus), f.ex. this polar equation: r = 2 sin(3*theta) ? I can convert this one: r = 16 cos(theta) knowing that: x = r cos(theta) and x^2 + y^2 = r^2 this comes to: x^2 + y^2 = 16x and the rest is plain algebra. Similar with sinus functions where y = r sin(theta). However, the 3 in the first example above is throwing me off. I know the answer is supposed to be: (x^2 + y^2)^2 = 6x^2y - 2y^3 but don't know how to get to it. Could someone explain this please?

knowing that: x = r cos(theta) and x^2 + y^2 = r^2 and y = r sin t