1. Given the sets $E=\left\{x \left\lvert\, x=\cos \frac{n \pi}{3}\right., n \in \mathbf{Z}\right\}, F=$ $\left\{x \left\lvert\, x=\sin \frac{(2 m-3) \pi}{6}\right., m \in \mathbf{Z}\right\}$. The relationship between $E$ and $F$ is ( ).
(A) $E \subset F$
(B)E $=F$
( C ) $E \supset F$
(D) $E \cap F=\varnothing$
-、1.(B).
Since the smallest positive period of the functions $x=\cos \frac{n \pi}{3}$ and $x=\sin \frac{(2 m-3) \pi}{6}$ is both 6, by taking $n, m=0, 1, 2, 3, 4, 5$, we get
$$
\begin{array}{l}
E=\left\{1, \frac{1}{2},-\frac{1}{2},-1\right\}, \\
F=\left\{-1,-\frac{1}{2}, \frac{1}{2}, 1\right\} .
\end{array}
$$