Answer
$\frac{\sqrt {15}}{8}$
Work Step by Step
1. $f(2\alpha)=sin(2\alpha)=2sin\alpha cos\alpha$
2. Use the given figures, we have $cos\alpha=-\frac{1}{4}, sin\alpha=-\frac{\sqrt {15}}{4},$
3. $f(2\alpha)=sin(2\alpha)=2(-\frac{\sqrt {15}}{4})(-\frac{1}{4})=\frac{\sqrt {15}}{8}$
