### Instruction: Compute $\arcsin (-1).$  Express your answer in radians.### Response: The inverse sine function, $\arcsin$, gives the angle whose sine is a given value, assuming it is in the range $[-\pi/2, \pi/2]$.
So, I need to find an angle $\theta$ such that $\sin \theta = -1$ and $\theta \in [-\pi/2, \pi/2]$.
I recall that the sine function is negative in the third and fourth quadrants, and that it reaches its minimum value of -1 at $\theta = -\pi/2$.