Answer
$\frac{\sqrt {15}}{8}$
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. $f(2\alpha)=sin(2\alpha)=2sin(\alpha)cos(\alpha)=2(-\frac{\sqrt {15}}{4})(-\frac{1}{4})=\frac{\sqrt {15}}{8}$