We are to find the positive and negative angles that are coterminal with
[tex]\frac{2\pi}{3}[/tex]
By definition
Coterminal Angles are angles that share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Hence,
The positive coterminal angle is
[tex]\frac{2\pi}{3}+2\pi[/tex]
Simplifying this we get
[tex]\begin{gathered} \frac{2\pi}{3}+2\pi \\ =\frac{2\pi+6\pi}{3} \\ =\frac{8\pi}{3} \end{gathered}[/tex]
Therefore, the positive coterminal angle is
[tex]\frac{8\pi}{3}[/tex]
The negative coterminal angle is
[tex]\begin{gathered} \frac{2\pi}{3}-2\pi \\ =\frac{2\pi-6\pi}{3} \\ =-\frac{4\pi}{3} \end{gathered}[/tex]
Therefore, the negative coterminal angle is
[tex]-\frac{4\pi}{3}[/tex]
