Trigonometry (10th Edition)

$cot$($\theta$ + 180$^{\circ}$) is negative in the interval (90$^{\circ}$,180$^{\circ}$).
$\theta$ is in the interval (90$^{\circ}$,180$^{\circ}$) Therefore: $\theta$ exists in Quadrant II. Therefore, $\theta$ + 180$^{\circ}$exists in Quadrant IV. All trigonometric functions are negative, in Quadrant IV, except for $\sec$ and $\cos$. Therefore $cot$($\theta$ + 180$^{\circ}$) is negative in the interval (90$^{\circ}$,180$^{\circ}$).