Answer:
The required angle is [tex]\frac{2\pi}{5}[/tex]
Step-by-step explanation
The given angle is [tex]\frac{52\pi}{5}[/tex].
To find a positive angle which is coterminal with [tex]\frac{52\pi}{5}[/tex] and is less than one revolution,
we subtract multiples of [tex]2\pi[/tex] until we obtain an angle between [tex]0\leq \theta\leq 2\pi[/tex].
Let the positive angle less than one revolution that is coterminal with [tex]\frac{52\pi}{5}[/tex] be [tex]\theta[/tex], then
[tex]\theta=\frac{52\pi}{5}-5(2\pi)[/tex],
We simplify to get,
[tex]\theta=\frac{52\pi}{5}-10\pi[/tex]
We collect LCM to obtain,
[tex]\theta=\frac{52\pi-50\pi}{5}[/tex]
[tex]\theta=\frac{2\pi}{5}[/tex]
The correct answer is A
