Evaluate \( \sin ^{-1}(-1) \)

The function \( \sin^{-1}(x) \), also known as arcsine, returns the angle whose sine is \( x \). For \( \sin^{-1}(-1) \), we are looking for an angle whose sine is \( -1 \). This occurs at \( \theta = -\frac{\pi}{2} \) or \( \theta = \frac{3\pi}{2} \). However, since the range of \( \sin^{-1}(x) \) is restricted to \( [-\frac{\pi}{2}, \frac{\pi}{2}] \), the valid answer is \( \sin^{-1}(-1) = -\frac{\pi}{2} \).