1. To obtain the graph of the function $y=\sin \left(2 x-\frac{\pi}{6}\right)$, the graph of the function $y=\cos 2 x$ can be ( ).
(A) shifted to the right by $\frac{\pi}{6}$ units
(B) shifted to the right by $\frac{\pi}{3}$ units
(C) shifted to the left by $\frac{\pi}{6}$ units
(D) shifted to the left by $\frac{\pi}{3}$ units
$$
\begin{array}{l}
\text {-1. B. } \\
y=\sin \left(2 x-\frac{\pi}{6}\right)=\cos \left[\frac{\pi}{2}-\left(2 x-\frac{\pi}{6}\right)\right] \\
=\cos \left(\frac{2 \pi}{3}-2 x\right)=\cos 2\left(x-\frac{\pi}{3}\right)
\end{array}
$$

It is easy to know that the graph of $y=\cos 2 x$ shifts to the right by $\frac{\pi}{3}$ units to become the graph of $y=\cos 2\left(x-\frac{\pi}{3}\right)$.