The period of the function $y = \sin 2x$ is

The period of $\sin \theta \cos \theta$ is

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3} - \cos \frac{\pi x}{2} + \tan \frac{\pi x}{4}$,$\beta$ be the period of $\sin^2 \left( \frac{\pi}{7} + \frac{x}{4} \right) - \sin^2 \left( \frac{\pi}{7} - \frac{x}{4} \right)$,and $\gamma$ be the period of $\cos^4 x + \sin^4 x$. Then $\frac{\alpha \gamma}{\beta} = $

The period of $f(x) = \sin \left( \frac{\pi x}{n - 1} \right) + \cos \left( \frac{\pi x}{n} \right)$,where $n \in \mathbb{Z}$ and $n > 2$,is:

If the period of the function $f(x) = 2 \cos(3x + 4) - 3 \tan(2x - 3) + 5 \sin(5x) - 7$ is $k$,then

The period of $|\sin 2x|$ is