You may have realized that the smallest positive value of x where $\displaystyle{y}={\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is at its maximum is at the end of one cycle, but gave the answer for the function $\displaystyle{y}={\cos{{x}}}\usepackage{cmbright}\Huge\$ . 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\$ .