Answer
$cos(2\theta) = -\frac{7}{25}$
Work Step by Step
If $90^{\circ} \lt \theta \lt 180^{\circ}$, then the angle $\theta$ is in quadrant II.
If the hypotenuse is 5, and the adjacent side has a length of 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$
$cos(2\theta) = cos^2~\theta -sin^2~\theta$
$cos(2\theta) = (-\frac{3}{5})^2 -(\frac{4}{5})^2$
$cos(2\theta) = \frac{9}{25} -\frac{16}{25}$
$cos(2\theta) = -\frac{7}{25}$
