Question

Find the Cartesian form of the equation, r3 = 3r cosØ

Answer 1

I will assume you meant

r^3 = 3r cosØ

Use: r^2 = x^2 + y^2 and x/r = cosØ

so if rcosØ = x
then 3rcosØ = 3x

and r^3 = r^2 r
= (x^2 + y^2)(x^2+y^2^(1/2)
= (x^2 + y^2)^(3/2)

r^3 + 3rcosØ ---> (x^2 + y^2)^(3/2) = 3x