Suppose $θ$ is in the interval $90^{\circ} < θ < 180^{\circ}$ . Find the sign of the following. $\cot (θ + 180^{\circ})$
Choose whether the sign of $\cot (θ + 180^{\circ})$ is positive or negative.
Positive
Negative

Answer

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Answer

Final Answer: The sign of $\cot (θ + 180^{\circ})$ is $Negative$ .

Steps

Step 1 ：Suppose $θ$ is in the interval $90^{\circ} < θ < 180^{\circ}$ . We need to find the sign of $\cot (θ + 180^{\circ})$ .

Step 2 ：The cotangent function is periodic with a period of $180^{\circ}$ . This means that $\cot (θ + 180^{\circ})$ is the same as $\cot (θ)$ .

Step 3 ：Since $θ$ is in the interval $90^{\circ} < θ < 180^{\circ}$ , $\cot (θ)$ is negative.

Step 4 ：Therefore, $\cot (θ + 180^{\circ})$ is also negative.

Step 5 ：Final Answer: The sign of $\cot (θ + 180^{\circ})$ is $Negative$ .