Answer
(a) See the graph.
(b) $x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$
Work Step by Step
(a)
$t=0$:
$x=cos^30=1$
$y=sin^30=0$
Point: $(1,0)$
$t=\frac{\pi}{2}$:
$x=cos^3\frac{\pi}{2}=0$
$y=sin^3\frac{\pi}{2}=1$
Point: $(0,1)$
$t=\pi$:
$x=cos^3\pi=-1$
$y=sin^3\pi=0$
Point: $(-1,0)$
$t=\frac{3\pi}{2}$:
$x=cos^3\frac{3\pi}{2}=0$
$y=sin^3\frac{3\pi}{2}=-1$
Point: $(0,-1)$
$t=2\pi$:
$x=cos^32\pi=1$
$y=sin^32\pi=0$
Point: $(1,0)$
(b)
$x=cos^3t$
$x^{\frac{2}{3}}=cos^2t$
$y=sin^3t$
$y^{\frac{2}{3}}=sin^2t$
$cos^2t+sin^2t=1$
$x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$
