#### Answer

$-\dfrac {\sqrt {45}}{7}$

#### Work Step by Step

$sec\theta =\dfrac {1}{\cos \theta }=\dfrac {7}{2}$ (positive)
$\tan \theta < 0$ (negative)
So angle is located in quadrant 4 ( sine is negative in quadrant 4)
$\Rightarrow \sin \theta =-\sqrt {1-\cos ^{2}\theta }=-\sqrt {1-\left( \dfrac {2}{7}\right) ^{2}}=-\dfrac {\sqrt {45}}{7}$