Answer
(a) See the graph
(b) $\frac{x^2}{4}+\frac{y^2}{9}=1$
Work Step by Step
(a)
Notice that, $0\leq t\leq2\pi$ is an entire period for both $sin~t$ and $cos~t$
$cos~0=1$ and $sin~0=0$
$cos~\frac{\pi}{2}=0$ and $sin~\frac{\pi}{2}=1$
$cos~\pi=-1$ and $sin~\pi=0$
$cos~\frac{3\pi}{2}=0$ and $sin~\frac{3\pi}{2}=-1$
$cos~2\pi=1$ and $sin~2\pi=0$
(b)
$x=2~cos~t$
$\frac{x}{2}=cos~t$
$\frac{x^2}{4}=cos^2t$
$y=3~sin~t$
$\frac{y}{3}=sin~t$
$\frac{y^2}{9}=sin^2t$
$cos^2t+sin^2t=1$
$\frac{x^2}{4}+\frac{y^2}{9}=1$
