If \( \alpha \) is a Quadrant \( I V \) angle with \( \cos (\alpha)=\frac{\sqrt{11}}{11} \), and \( \sin (\beta)=\frac{\sqrt{2}}{2} \), where \( \frac{\pi}{2}<\beta<\pi \), find
(a) \( \sin (\alpha+\beta) \) \( \square \)
(b) \( \cos (\alpha-\beta) \) \( \square \)