For the polar equation r3 sin what is its Cartesian equation

For the polar equation r=3 sin, what is its Cartesian equation?

Solution

r = sqrt(x^2 + y^2)

sin(theta) = y/r

r=3 sin

sqrt(x^2 + y^2) = 3y/r

Mulitply both sides:

sqrt(x^2 + y^2)*sqrt(x^2 + y^2) = 3y

(x^2 + y^2) = 3y

x^2 + y^2 - 3y =0

x^2 + y^2 - 3y +9/4 -9/4 =0

x^2 + (y -3/)^2 = 9/4

Equation of circle with centre ( 0, 3) ; radius = 3/2