Use reference angles to find the exact value of the following expression. \( \cot \left(-\frac{\pi}{4}\right) \) Select the correct choice below and, if necessary, fill in the answer box to, complete your choice. A. \( \cot \left(-\frac{\pi}{4}\right)=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expressi) the denominator.) B. The answer is undefined.

To find the exact value of \( \cot \left(-\frac{\pi}{4}\right) \) using reference angles, we first need to determine the reference angle for \( -\frac{\pi}{4} \). The reference angle for \( -\frac{\pi}{4} \) is \( \frac{\pi}{4} \) because \( -\frac{\pi}{4} \) is in the fourth quadrant, and the reference angle is the acute angle formed between the terminal side of the angle and the x-axis. Now, we know that \( \cot \theta = \frac{1}{\tan \theta} \). So, we can find \( \cot \left(-\frac{\pi}{4}\right) \) by finding \( \tan \left(-\frac{\pi}{4}\right) \) and then taking the reciprocal. The tangent of \( -\frac{\pi}{4} \) is \( -1 \) because \( \tan \left(-\frac{\pi}{4}\right) = -1 \). Therefore, \( \cot \left(-\frac{\pi}{4}\right) = \frac{1}{-1} = -1 \). So, the correct choice is: A. \( \cot \left(-\frac{\pi}{4}\right) = -1 \)