Suppose $\theta$ is in the interval $90^{\circ}< \theta< 180^{\circ}$. Find the sign of the following. $\cot \left(\theta+180^{\circ}\right)$
Choose whether the sign of $\cot \left(\theta+180^{\circ}\right)$ is positive or negative.
Positive
Negative
Answer
Final Answer: The sign of $\cot \left(\theta+180^\circ\right)$ is \(\boxed{\text{Negative}}\).
Step 1 ：Suppose $\theta$ is in the interval $90^\circ<\theta<180^\circ$. We need to find the sign of $\cot \left(\theta+180^\circ\right)$.
Step 2 ：The cotangent function is periodic with a period of $180^\circ$. This means that $\cot \left(\theta+180^\circ\right)$ is the same as $\cot \left(\theta\right)$.
Step 3 ：Since $\theta$ is in the interval $90^\circ<\theta<180^\circ$, $\cot \left(\theta\right)$ is negative.
Step 4 ：Therefore, $\cot \left(\theta+180^\circ\right)$ is also negative.
Step 5 ：Final Answer: The sign of $\cot \left(\theta+180^\circ\right)$ is \(\boxed{\text{Negative}}\).
