Answer
$\sqrt {\frac{5-\sqrt 5}{10}}$
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. $g(\frac{\theta}{2})=cos(\frac{\theta}{2})=\sqrt {\frac{1+cos\theta}{2}}=\sqrt {\frac{1-\frac{\sqrt 5}{5}}{2}}=\sqrt {\frac{5-\sqrt 5}{10}}$