What is \( \sin ^{-1}\left(\frac{-1}{2}\right) \) in radians? You can use the letter \( p \) to indicate pi.

The value of \( \sin^{-1}\left(\frac{-1}{2}\right) \) corresponds to an angle whose sine is \(-\frac{1}{2}\). In the unit circle, this happens at \( -\frac{\pi}{6} \) radians, which is equivalent to \(-30^\circ\). Remember, the inverse sine function typically yields results in the range of \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\). Another way to think about this is that the sine function is negative in the fourth quadrant. Since the sine of \(-\frac{\pi}{6}\) gives us \(-\frac{1}{2}\), we confirm that \( \sin^{-1}\left(\frac{-1}{2}\right) = -\frac{\pi}{6} \). So, there you have it: the answer in radians is \( -\frac{\pi}{6} \).