Eliminate t to give an equation that relates x and y:
x=cos(t)y=sin2(t)−3
y= ??
Remember the identity:
$\displaystyle \sin^2{t} + \cos^2{t} = 1$
So:
$\displaystyle sin^2{t} = 1 - \cos^2{t}$
$\displaystyle y = 1 - \cos^2{t} - 3$
$\displaystyle y = -\cos^2{t} - 2$
Now we look at x:
$\displaystyle x = \cos{t}$
Square both sides:
$\displaystyle x^2 = \cos^2{t}$
Multiply both sides by -1:
$\displaystyle -x^2 = -\cos^2{t}$
Now, subtract both sides by 2:
$\displaystyle -x^2 - 2 = -\cos^2{t} - 2$
We know that:
$\displaystyle y = -\cos^2{t} - 2$
So, we get:
$\displaystyle y = -x^2 - 2$
And there you go.