Answer
$ -\frac{\sqrt {2-\sqrt 3}}{2}$
Work Step by Step
$sin(-\frac{\pi}{12})=-sin(\frac{\pi}{12})=-sin(\frac{\pi/6}{2})
=-\sqrt {\frac{1-cos(\pi/6)}{2}}
=-\sqrt {\frac{1-\sqrt 3/2}{2}}
=-\frac{\sqrt {2-\sqrt 3}}{2}$
Note: this is the same as $-\frac{\sqrt 6-\sqrt 2}{4}$
