The easiest way to solve this problem is to substract 2π from the angle until we get an angle that is less than 2π.
[tex]\frac{19}{3}\pi-2\pi=\frac{19-6}{3}\pi=\frac{13}{3}\pi[/tex]
13/3π is not less than 2π, so we have to substract 2π once more:
[tex]\frac{13}{3}\pi-2\pi=\frac{13-6}{3}\pi=\frac{7}{3}\pi[/tex]
7/3π is still not less than 2π, substract 2π once more:
[tex]\frac{7}{3}\pi-2\pi=\frac{7-6}{3}\pi=\frac{1}{3}\pi[/tex]
1/3π is less than 2π. It means that the positive angle less than 2π that is coterminal with 19/3π is 1/3π.
