## Precalculus (6th Edition)

RECALL: The quadrantal angles are: Positive x-axis: $0$ radians; Positive y-axis: $\frac{3.14}{2} = 1.57$ radians; Negative x-axis: $3.14$ radians; Negative y-axis: $4.61$ radians Positive x-axis: $6.18$ radians Thus, when moving counterclockwise from the positive x-axis, the angle $5$ radians is beyond the negative y-axis but before the positive x-axis. This means that the angle is in Quadrant IV. With $\sin{\theta}=y$, and since the value of $y$ is negative in Quadrant IV, then $\sin{5}$ must be negative.