If $\sin( 2 \theta) = \cos( 3)$ and $\theta \leq 90°$, find $\theta$ Find $\theta\leq90°$ if 
$$\sin( 2 \theta) = \cos( 3)$$
I know that $\sin 2\theta = 2\sin\theta\cos \theta$, or alternatively, $\theta = \dfrac{\sin^{-1}(\cos 3)}{2}$.
Can somebody help me?

Assuming you mean $3^{\circ}$, here are the steps
$$ \sin 2\theta=\cos 3^{\circ} $$
$$ \arcsin(\sin 2\theta)=\arcsin(\cos 3^{\circ}) $$
$$ 2\theta=\arcsin(\cos 3^{\circ}) $$
$$ \theta=\frac{1}{2}\arcsin(\cos 3^{\circ})=\frac{87^{\circ}}{2}=43.5^{\circ} $$
