Answer
$c$
Work Step by Step
$\sec{\theta} = -\sqrt{1+\tan^2{\theta}} = -\sqrt{1+(-\dfrac{1}{2})^2} = -\dfrac{\sqrt{5}}{2}$
$\cos{\theta} =\dfrac{1}{\sec{\theta}} = - \dfrac{2\sqrt{5}}{5}$
$\sin{\theta} =\sqrt{1-\cos^2{\theta}} =\dfrac{\sqrt{5}}{5}$
$\sin{2\theta} = 2 \sin{\theta} \cos{\theta} = -\dfrac{4}{5}$
