Question

Find a rectangular-coordinate equation for the curve by eliminating the parameter. x=cos^3(t)  y=sin^3(t)   o <= t <= 2pi 

Answer 1

$x=\cos^3t\implies x^{2/3}=(\cos^3t)^{2/3}=\cos^2t$

SImilarly,

$y=\sin^3t\implies y^{2/3}=\sin^2t$

So recalling that $\cos^2t+\sin^2t=1$, you end up with the rectangular form

$x^{2/3}+y^{2/3}=1$