To find a coterminal angle, we subtract or add on 360. This rotates the angle one full revolution. We see that 470 is not in the interval [tex]0^{\circ} < \theta < 360^{\circ}[/tex], as its too large. Subtract off 360 to get
470-360 = 110
The angle 110 degrees is in the interval [tex]0^{\circ} < \theta < 360^{\circ}[/tex]
Therefore, the angle 110 degrees is coterminal to 470 degrees. In other words, both angles (110 and 470 degrees) point in the exact same direction. They point in the same direction because the angle has rotated one full revolution, so that's why there is no change in direction.
