Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 60: 70

$cos$ (-$\theta$) is negative in the interval (90$^{\circ}$,180$^{\circ}$).

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