Answer
$-\frac{\sqrt {6}}{4}$
Work Step by Step
1. Use the given figures, we have $cos\alpha=-\frac{1}{4}, sin\alpha=-\frac{\sqrt {15}}{4},$
2. $g(\frac{\alpha}{2})=cos(\frac{\alpha}{2})=-\sqrt {\frac{1+cos\alpha}{2}}=-\sqrt {\frac{1-\frac{1}{4}}{2}}=-\frac{\sqrt {6}}{4}$
