#### Answer

$-\dfrac {\sqrt {117}}{11}$

#### Work Step by Step

$sec\theta =\dfrac {1}{\cos \theta }=\dfrac {11}{4}$ (positive)
$\cot \theta < 0$ ( negative)
So angle is located in quadrant 4(sine is negative in quadrant 4)
$\Rightarrow \sin \theta =-\sqrt {1-\cos ^{2}\theta }=-\sqrt {1-\left( \dfrac {4}{11}\right) ^{2}}=-\dfrac {\sqrt {117}}{11}$