Answer
$\cos{\theta} = -\dfrac{1}{2}$
Work Step by Step
RECALL:
Since the cosine and secant functions are reciprocals of each other, then $\cos{\theta} = \dfrac{1}{\sec{\theta}}$.
Thus, if $\sec{\theta} = -2$, then
$\cos{\theta} = \dfrac{1}{\sec{\theta}} = \dfrac{1}{-2} = -\dfrac{1}{2}$
