Answer:
The coterminal angle is [tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
In order to find a positive coterminal angle, we must have to add [tex]2\pi[/tex] to the angle:
[tex]2\pi + (-\frac{4\pi}{3})=2\pi -\frac{4\pi}{3}[/tex]
Applying the rule for substraction of an integer and a fraction:
[tex]a-\frac{b}{c} = \frac{(a)(c)-b}{c}[/tex]
In this case:
[tex]a=2\pi\\b=4\pi\\c=3[/tex]
Therefore:
[tex]2\pi-\frac{4\pi}{3}=\frac{(2\pi)(3)-4\pi}{3}=\frac{6\pi-4\pi}{3}=\frac{2\pi}{3}[/tex]
