Answer
$-\frac{\sqrt {6}}{4}$
Work Step by Step
Step 1. Using the given figures, we have $a=-\sqrt {5-4}=-1, b=-\sqrt {1-\frac{1}{16}}=-\frac{\sqrt {15}}{4}$
Step 2. $g(\frac{\alpha}{2})=cos(\frac{\alpha}{2})=-\sqrt {\frac{1+cos\alpha}{2}}=-\sqrt {\frac{1+(-1/4)}{2}}=-\frac{\sqrt {6}}{4}$
