If $\sin 2x =\frac{5}{13}$ and $0^\circ < x < 45^\circ$, find $\sin x$ and $\cos x$.
The answers should be $\frac{\sqrt{26}}{26}$ and $\frac{5\sqrt{26}}{26}$
Ideas
The idea is to use double angle identities. One such identity is $\sin 2x=2\sin x\cos x$.
It's easy to use it to find $\sin 2x$ from known $\sin x$ and $\cos x$. But here it's the other way around.
Best Answer
Because we know $\sin(2x) = 2\sin(x)\cos(x)$, it is like solving an equation: $u^2+v^2 = 1$ and $2uv = 5/13$, $u = \sin(x)$ and $v = \cos(x)$. Hope this helps.
EDIT: oh don't forget to take only the positive roots.