\( \left[\begin{array}{l}\text { Select your answer } \\ \text { Simplify } \cot \left(\frac{3 \pi}{4}\right) \\ -\infty \\ -1 \\ 0 \\ 1\end{array}\right. \)

Calculate the value by following steps: - step0: Calculate: \(\cot\left(\frac{3\pi }{4}\right)\) - step1: Rewrite the expression: \(-\cot\left(\frac{\pi }{4}\right)\) - step2: Calculate: \(-1\) To simplify \( \cot\left(\frac{3\pi}{4}\right) \): 1. Recall that \( \cot(x) = \frac{\cos(x)}{\sin(x)} \). 2. Calculate \( \cos\left(\frac{3\pi}{4}\right) \) and \( \sin\left(\frac{3\pi}{4}\right) \): - \( \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} \) - \( \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} \) 3. Now, substitute these values into the cotangent function: \[ \cot\left(\frac{3\pi}{4}\right) = \frac{\cos\left(\frac{3\pi}{4}\right)}{\sin\left(\frac{3\pi}{4}\right)} = \frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = -1 \] Thus, the simplified value of \( \cot\left(\frac{3\pi}{4}\right) \) is \(-1\). The correct answer is \(-1\).