1. As shown in the figure, in the cube $A C_{1}$, $M, N$ are the midpoints of edges $C_{1} D_{1}, A B$ respectively, and points $A_{1}, M, C, N$ lie in the same plane. The sine value of the angle formed by $C D$ and the plane $A_{1} M C N$ is
A. $\frac{1}{2}$
B. $\frac{\sqrt{3}}{2}$
C. $\frac{\sqrt{6}}{3}$
D. $\frac{\sqrt{2}}{4}$
1. C As shown in the figure, from the given conditions, we know that quadrilateral $A_{1} M C N$ is a rhombus,

so $A_{1} C$ bisects $\angle M A_{1} N$ and $\angle M C N$,
also, since $\angle D C N=\angle M C D$, that is, $C D$ forms equal angles with the two sides of $\angle M C N$, the projection of line $C D$ in the plane $M C N$ is $A_{1} C$, thus $\angle D C A_{1}$ is the angle formed by $C D$ and the plane $A_{1} M C N$. It is easy to know that $\sin \angle D C A_{1}=\sqrt{\frac{2}{3}}$ is the required value.