This has the general shape of the graph of a cosine function. The amplitude of this graph and $\displaystyle{y}={4}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is 4. This graph has 1 cycle on the interval $\displaystyle{\left[{0},{4}\pi\right]}\usepackage{cmbright}\Huge\$ , so it has a period of $\displaystyle{4}\pi\usepackage{cmbright}\Huge\$ . The function $\displaystyle{y}={4}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ has a period of

$\displaystyle\frac{{{2}\pi}}{{\frac{{1}}{{2}}}}=\frac{{{2}\pi}}{{1}}\cdot\frac{{2}}{{1}}={4}\pi\usepackage{cmbright}\Huge\$ .

So the graph and the function match.