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`