This has the repeating hill and valley pattern of the graph of a cosine function. The amplitude of this graph and $\displaystyle{y}=\frac{{3}}{{2}}{\cos{{4}}}{x}\usepackage{cmbright}\Huge\$ is $\displaystyle\frac{{3}}{{2}}\usepackage{cmbright}\Huge\$ . This graph has 2 cycles on the interval $\displaystyle{\left[{0},\pi\right]}\usepackage{cmbright}\Huge\$ , so a period of $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ .

The function $\displaystyle{y}=\frac{{3}}{{2}}{\cos{{4}}}{x}\usepackage{cmbright}\Huge\$ has a period of $\displaystyle\frac{{{2}\pi}}{{4}}=\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ . So the graph and the function match.