If there is a parametric equation $x=2\cos{2t}$ and $y=6\sin{t}$, $0\le t \le \frac{\pi}{2}$ the Cartesian equation is $y=3\sqrt{2-x}$.
How do I find the domain of the Cartesian equation? I tried:
$$0\le t \le \frac{\pi}{2}$$ $$2\cos{2(0)}\le 2\cos{2t} \le 2\cos{2(\frac{\pi}{2})}$$ $$2\cos{0}\le x \le 2\cos\pi$$ $$2(1)\le x \le 2(-1)$$ $$2\le x \le-2$$
Which can't be true, as both inequalities can't be satisfied at the same time?
When $0\leq t\leq\pi/2$ then $0\leq2t\leq\pi$. Between $0$ and $\pi$ the function of cosine is decreasing so $$\cos(\pi)\leq\cos(2t)\leq\cos(0)$$ or $$-1\leq\cos(2t)\leq 1$$ then $$-2\leq2\cos(2t)\leq 2$$ or $$-2\leq x\leq 2$$.