Compute $\arcsin (-1).$  Express your answer in radians.
We can look at the unit circle to find the angle whose sine is $-1$. The sine is negative in the third and fourth quadrants, so we want an angle that is in one of those two quadrants and has a sine of $1$. The angle $270^\circ$ is in the third quadrant and has a sine of $1$. So the arcsine of $-1$ is $270^\circ$. But the question wants the answer in radians, so we need to convert. There are $2\pi$ radians in a circle, so an angle of $270^\circ$ is $\frac{270}{360} \cdot 2\pi = \frac{3\pi}{2}$ radians. Right, so the answer is actually $\frac{-\pi}{2}$.

