Answer
$ - \dfrac{\sqrt{{2-\sqrt2}}}{2}$
Work Step by Step
The half-angle Identity for sine can be expressed as:
$\sin {(\dfrac{\theta}{2})}=\pm\sqrt{\dfrac{1-\cos{\theta}}{2}}$
Since, $\sin (-a )=-\sin a$
Therefore, $\sin (-\dfrac{\pi}{8})=- \sqrt{\dfrac{1-\cos(-\dfrac{\pi}{4})}{2}} \\=- \sqrt{\dfrac{1-\dfrac{\sqrt2}{2}}{2}}\\=- \sqrt{\dfrac{2-\sqrt2}{4}}\\ = - \dfrac{\sqrt{{2-\sqrt2}}}{2}$