Evaluate the expression. Answer in radians. \( \tan ^{-1}(-1)=\square \)

The expression \( \tan^{-1}(-1) \) corresponds to the angle whose tangent is \(-1\). The principal value of \( \tan^{-1}(x) \) is typically in the range \(-\frac{\pi}{2} < y < \frac{\pi}{2}\). Since the tangent of \(-\frac{\pi}{4}\) is \(-1\), we have \( \tan^{-1}(-1) = -\frac{\pi}{4} \). Additionally, it's useful to remember that the tangent function is periodic, repeating every \(\pi\) radians. Thus, while \(-\frac{\pi}{4}\) is one valid answer, other equivalent angles in the broader context include values like \( \frac{3\pi}{4} + k\pi \) for integers \(k\). However, in the context of principal values, we keep it as \(-\frac{\pi}{4}\).