Finding Coterminal Angles Using Radians

When working in degrees, we found coterminal angles by adding or subtracting 360 degrees, a full rotation. Likewise, in radians, we can find coterminal angles by adding or subtracting full rotations of $2\pi$ radians:

The angle $\frac{11\pi }{4}$ is coterminal, but not less than $2\pi ,$ so we subtract another rotation.

The angle $\frac{3\pi }{4}$ is coterminal with $\frac{19\pi }{4},$ as shown in Figure 20.