[tex]f(2\pi)=\cos (2\pi)=1[/tex][tex]\begin{gathered} 1\text{ is the biggest value of cos}\theta.\text{ And within the interval (0, 2}\pi),\text{ } \\ \text{cos}\theta=1 \\ at\text{ }\theta=0\text{ or 2}\pi \\ \end{gathered}[/tex]
Hence the correct choice is
(2π, 1)