The cosine function has its maximum value at $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ and then again at the end of one cycle. The value of x at that point is the length of one cycle, or one period of $\displaystyle{y}={\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ . You may have realized this but miscalculated the period. Remember that the period of $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ is $\displaystyle\frac{{{2}\pi}}{{\left|{b}\right|}}\usepackage{cmbright}\Huge\$ .