Answer
(a) See the graph.
(b)
$y=2x^2-1,~~-1\leq x\leq1$
Work Step by Step
(a) $x=cos~t$ and $y=cos~2t$ are periodic functions. The maximum value of $cos~t$ is $1$ and the minimum is $-1$. In these points $x=cos~t$ change the directions. That is, $x$ and $y$ move back and forth from $(-1,1)$ to $(1,1)$.
(b)
$x=cos~t~~$ ($-1\leq x\leq1$)
$x^2=cos^2t$
Use:
$cos^2t+sin^2t=1$
$cos^2t-1=-sin^2t$
$y=cos~2t=cos^t-sin^2t=cos^2t+cos^2t-1=2cos^2t-1$
$y=2x^2-1,~~-1\leq x\leq1$
