Intersection of $y=a\sin2x$ and $y=\sin x$ Two graphs $y=a\sin2x$ and $y=\sin x$ are intersecting on $[0,\pi$].
Find a.
What I did:
$a\sin2x=\sin x$
$\sin x(2a\cos x-1)=0$
$\sin x=0$ (doesn't fit the criteria)
$2a\cos x-1=0$
$\cos x= \frac{1}{2a}$
In solutions says that a is $|a|> \frac{1}{2}$. How did they get that? Does anybody have any suggestions?

It's simple if you remember that $|\cos x|\le 1$, so you must have
$$
\frac{1}{2|a|}\le1
$$
which is equivalent to
$$
|a|\ge\frac{1}{2}.
$$
You can multiply both sides by $|a|$ because it's a positive number (it can't obviously be $0$).
