Question

Determine the Cartesian form of the equation r^2 cos theta -cos3theta

Answer 1

I see no equation. Maybe you mean

r^2 cosθ = cos(3θ)
r^2 cosθ = 4cos^3(θ) - 3cosθ
r^2 = 4cos^2θ - 3
r^2 = 4(x/r)^2 - 3
x^2+y^2 = 4x^2/(x^2+y^2) - 3
(x^2+y^2)^2 + 3(x^2+y^2) - 4x^2 = 0

do with that what you will.