If $x=a$·co$s^3$θ and $y=b$·si$n^3$θ, the relation between $x$ and $y$ that no longer contains θ is:

Take the cube root first: $(x/a{)}^{1/3}$ = cosθ and $(y/b{)}^{1/3}$ = sinθ. Squaring and adding kills θ through co$s^2$θ + si$n^2$θ = 1, which leaves the two-thirds powers. Squaring the ratios directly (the third choice) would only be right for $x=a$·cosθ, and inverting the exponent to 3/2 undoes the cube in the wrong direction.