Answer
$-0.4$
Work Step by Step
$115^{\circ}$ is in between $90^{\circ}$ and $180^{\circ}$ and therefore it is in quadrant II. In the second quadrant, the value of $\cos\theta$ is negative.
$\cos115^{\circ}=-\cos(180^{\circ}-115^{\circ})=-\cos65^{\circ}$
We know that the value of $-\cos60=-\frac{1}{2}=-0.5$
We expect the value of $-\cos 65^{\circ}$ to be greater but closer to $-\cos60^{\circ}$ (as $-\cos0^{\circ}=-1$ and $-\cos90^{\circ}=0$) and therefore -0.4 should be closest to $\cos 115^{\circ}$.
