1. If $M=\left\{(x, y) \| \tan \pi y \mid+\sin ^{2} \pi x=0\right\}, N=\left\{(x, y) \| x^{2}+y^{2} \mid \leqslant 2\right\}$, then the number of elements in $M \cap N$ is
(A) 4
(B) 5
(C) 8
(D) 9
(D)
I. Multiple Choice Question
1.【Analysis and Solution】From $\tan \pi y=0$ we get $y=k(k \in \mathbf{Z})$, and from $\sin \pi x=0$ we get $x=k^{\prime}\left(k^{\prime} \in \mathbf{Z}\right)$.
$$
\begin{array}{l}
\text { Also } x^{2}+y^{2} \leqslant 2 \\
\therefore k=-1,0,1 ; \\
k^{\prime}=-1,0,1 .
\end{array}
$$

As shown in the figure, there are a total of 9 points, so the answer is (D).