You probably made a mistake with the calculation of the period.

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\$ .

However, this graph has 4 cycles in the interval $\displaystyle{\left[{0},\pi\right]}\usepackage{cmbright}\Huge\$ , so a period of $\displaystyle\frac{\pi}{{4}}\usepackage{cmbright}\Huge\$ . But $\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\$ .