Answer
$x^{2}+y^{2}=1$
Work Step by Step
$x=\cos 2t\Rightarrow\quad \left[\begin{array}{ll}
t & x\\
0 & 1\\
\pi/4 & 0\\
\pi/2 & -1\\
3\pi/4 & 0\\
\pi & 1
\end{array}\right]\Rightarrow\quad-1 \leq x \leq 1$
Square both parametric equations: $\left\{\begin{array}{l}
x^{2}=\cos^{2}2t\\
y^{2}=\sin^{2}2t
\end{array}\right.$
Add the two equations:
$ \fbox{$ x^{2}+y^{2}=1 $}$
To graph, create a table using several values for $t$, and then calculate $(x(t), y(t)),$ plotting the points as you go. Join with a smooth curve, noting the direction in which $t$ increases.
