1. The problem is to find the period of the function $\sin 2x$. 2. Recall that the general form of the sine function is $\sin bx$, where $b$ affects the period. 3. The period of $\sin x$ is $2\pi$. 4. For $\sin bx$, the period is given by the formula: $$\text{Period} = \frac{2\pi}{|b|}$$ 5. In this problem, $b = 2$. 6. Substitute $b = 2$ into the formula: $$\text{Period} = \frac{2\pi}{2} = \pi$$ 7. Therefore, the period of $\sin 2x$ is $\pi$. This means the function $\sin 2x$ repeats its values every $\pi$ units along the x-axis.