Suppose $\theta$ is in the interval $\left(90^{\circ}, 180^{\circ}\right)$. Find the sign of the following.
\[
\cos (-\theta)
\]
Choose whether the sign of $\cos (-\theta)$ is positive or negative.
Negative
Positive

Step 1 ：Suppose \(\theta\) is in the interval \((90^\circ, 180^\circ)\). We are asked to find the sign of \(\cos (-\theta)\).

Step 2 ：The cosine function has the property of being even, which means that \(\cos(-\theta) = \cos(\theta)\). Therefore, the sign of \(\cos(-\theta)\) is the same as the sign of \(\cos(\theta)\).

Step 3 ：Since \(\theta\) is in the interval \((90^\circ, 180^\circ)\), \(\cos(\theta)\) is negative because cosine is negative in the second quadrant. Therefore, \(\cos(-\theta)\) is also negative.

Step 4 ：Let's confirm this with a specific example. Let \(\theta = 150\).

Step 5 ：Converting \(\theta\) to radians, we get \(\theta_{\text{rad}} = 2.6179938779914944\).

Step 6 ：Calculating \(\cos(-\theta)\), we get \(\cos_{\text{neg}_\theta} = -0.8660254037844387\).

Step 7 ：This confirms our initial thought. The value of \(\cos(-\theta)\) is negative when \(\theta\) is in the interval \((90^\circ, 180^\circ)\).

Step 8 ：Final Answer: The sign of \(\cos(-\theta)\) is \(\boxed{\text{Negative}}\).