## Precalculus (6th Edition) Blitzer

$\frac{\sqrt {2-\sqrt 2}}{2}$
Use the half-angle formula $sin\frac{u}{2}=\pm\sqrt {\frac{1-cos(u)}{2}}$; for $\frac{u}{2}=22.5, u=45$, choose the positive sign to get $sin22.5=\sqrt {\frac{1-cos(45)}{2}}=\sqrt {\frac{1-\sqrt 2/2}{2}}=\frac{\sqrt {2-\sqrt 2}}{2}$