什么是三角函数---17. (12 分) 如图, 在四棱锥 P - ABCD 中, 底面 ABCD 为正方形, PA⊥平面 ABCD, M, N 分别为棱 PD, BC 的中点, PA = AB = 2. (I) 求证: MN // 平面 PAB; (II) 求直线 MN 与平面 PCD 所成角的正弦值. --- **Chart/Diagram Description:** * **Type:** 3D geometric diagram representing a pyramid. * **Main Elements:** * **Pyramid:** P-ABCD. * **Base:** ABCD, depicted as a square in perspective view. Vertices are labeled A, B, C, D. * **Apex:** P. * **Edges:** PA, PB, PC, PD, AB, BC, CD, DA. * **Points:** * P: Apex of the pyramid. * A, B, C, D: Vertices of the square base. * M: A point located on edge PD, appearing to be the midpoint. * N: A point located on edge BC, appearing to be the midpoint. * **Lines:** * Solid lines: Visible edges (PB, PC, PD, BC, CD). * Dashed lines: Hidden edges (PA, AB, AD) and the line segment MN connecting M and N. * **Relative Position and Direction:** P is above the base ABCD. PA is depicted as a vertical line segment from P to A on the base. A, B, C, D are arranged in counterclockwise order (from top-left: A, top-right: B, bottom-right: C, bottom-left: D in the depicted perspective, but described as a square base ABCD). M is on PD, N is on BC. * **Labels:** Vertices P, A, B, C, D, and points M, N are labeled.