You probably made a mistake with the calculation of the period. The amplitude of this graph and $\displaystyle{y}={4}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ is 4. However, this graph has half a cycle in the interval $\displaystyle{\left[{0},{2}\pi\right]}\usepackage{cmbright}\Huge\$ , so a period of $\displaystyle{4}\pi\usepackage{cmbright}\Huge\$ . But $\displaystyle{y}={4}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ has a period of $\displaystyle\pi\usepackage{cmbright}\Huge\$ .