Vector Cosine

$$\cos(\theta_{xy}) \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;\frac{\left<x,y\right>}{\Vert x\Vert\cdot\Vert y\Vert} \;=\;\frac{\left<X,Y\right>}{\Vert X\Vert\cdot\Vert Y\Vert}$$