## Precalculus (6th Edition)

A negative angle means the measurement is taken by moving clockwise from the positive x-axis. Note that the negative y-axis is $\frac{\pi}{2}$ radians (or $1.57$ radians) clockwise from the positive x-axis. This means that the angle $-1$ radians is in Quadrant IV. With $\sin{\theta}=y$, and since $y$ is negative in Quadrant IV, then $\sin{(-1)}$ must be negative.