$\noindent This is a special case. Do you know the Unit Circle? \\ For the ''how?'': it's basically because $\cos$ has roots at $x= 0, \pi/2,-\pi,2$. From what you know, $\cos$ has periodicity $2\pi$. Then since $x=\pi/2,-\pi/2$ are roots, then $x=\pi/2 - 2\pi,-\pi/2 + 2\pi$ are roots as well...