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