Answer:
The angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]Explanation:
We want to find the angle between 0 and 2 pie that is coterminal to;
[tex]\frac{34}{7}\pi[/tex]Angles that are coterminal with the given angle can be calculated using the formula;
[tex]x+n2\pi=\frac{34}{7}\pi[/tex]Where n=1,2,3...
and x is the coterminal angle.
At n = 1;
[tex]\begin{gathered} x+2\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-2\pi \\ x=\frac{34}{7}\pi-\frac{14}{7}\pi \\ x=\frac{20}{7}\pi \end{gathered}[/tex]at n=2;
[tex]\begin{gathered} x+2(2\pi)=\frac{34}{7}\pi \\ x+4\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-4\pi \\ x=\frac{34}{7}\pi-\frac{28}{7}\pi \\ x=\frac{6}{7}\pi \end{gathered}[/tex]At n=2;
The value of x is between 0 and 2pie;
So, the angle between 0 and 2 pie that is coterminal to the given angle is;
[tex]\frac{6}{7}\pi[/tex]