Answer:
[tex]coterminal\text{ angle}=\frac{2\pi}{3}[/tex]
Explanations
The coterminal of angle is determined by adding or subtracting 360 degrees (2pi) from the reference angle.
Given the reference angle in radians as shown:
[tex]\frac{14\pi}{3}[/tex]
Subtract 360 degerees (2π) from the angle to have
[tex]\begin{gathered} \frac{14\pi}{3}-2\pi=\frac{14\pi-6\pi}{3}=\frac{8\pi}{3} \\ \end{gathered}[/tex]
Subtract 2π from the result to have:
[tex]\frac{8\pi}{3}-2\pi=\frac{8\pi-6\pi}{3}=\frac{2\pi}{3}[/tex]
Hence the coterminal angle that lies between 0 and 2π radians is 2π/3 rad
