This graph passes through the origin and has a hill to the right of the y-axis, so it could be a sine function. The amplitude of this graph and $\displaystyle{y}=\frac{{3}}{{2}}{\sin{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is $\displaystyle\frac{{3}}{{2}}\usepackage{cmbright}\Huge\$ . This graph has half of a cycle in the interval $\displaystyle{\left[{0},{2}\pi\right]}\usepackage{cmbright}\Huge\$ , or a period of $\displaystyle{4}\pi\usepackage{cmbright}\Huge\$ . The same is true for $\displaystyle{y}=\frac{{3}}{{2}}{\sin{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ , so the graph and the function match in all of these respects.