#### Answer

$=-\dfrac {2\sqrt {5}}{5}$

#### Work Step by Step

Cosine is even function so
$\cos \left( -\theta \right) =\dfrac {\sqrt {5}}{5}\Rightarrow \cos \theta =\dfrac {\sqrt {5}}{5}$
We see that $\cos \theta $ is positive and $\tan \theta $ is negative so angle is located in quadrant 4 and sine function is negative in quadrant 4
$\Rightarrow \sin \theta =-\sqrt {1-\cos ^{2}\theta }=-\sqrt {1-\left( \dfrac {\sqrt {5}}{5}\right) ^{2}}=-\dfrac {2\sqrt {5}}{5}$