Consider the parametric curve: $$x=6\cos^3(t), y=6\sin^3(t)$$ Write it in Cartesian form.
I am really struggling with the solution for this. I've been trying to find $t$ from $x$, and then plugging that into $y$, but it ends up being too complicated.
It is asked to be put in the form $F(x,y)=c$, for some function $F,$ and some constant $c$.
Any help at all would be appreciated, thank you.
Best Answer
solving for $t,$ you get $$\cos t = \left(\frac x6\right)^{1/3} , \, \sin t = \left(\frac y6\right)^{1/3} $$ now use the fact $$\sin^2 t + \cos ^2 t = 1 \to \left(\frac x6\right)^{2/3} + \left(\frac y6\right)^{2/3} = 1$$