Answer
$y=1-2x^{2},\ \ x\in[-1,1]$
Work Step by Step
From the parametric equation for x, we see that $x\in[-1,1].$
Using a double angle identity formula for cosine,
$\cos 2t=1-2\sin^{2}t$
substituting,
$y=1-2x^{2}\quad $... (a parabola that opens down)
From the parametric equation for x, we see that $x\in[-1,1],$ so we restrict the Cartesian equation:
$y=1-2x^{2},\ \ x\in[-1,1]$
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
