Answer
$-\frac{4}{5}$
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. $f(2\theta)=sin(2\theta)=2sin\theta cos\theta=2(\frac{2\sqrt 5}{5})(-\frac{\sqrt 5}{5})=-\frac{4}{5}$
