You seem to have confused the roles of a and b. The amplitude of $\displaystyle{y}={3}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ is 3, while the amplitude of the graph is 2. The period of $\displaystyle{y}={3}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ is $\displaystyle\pi\usepackage{cmbright}\Huge\$ , while the period of the function in the graph is $\displaystyle\frac{{{2}\pi}}{{3}}\usepackage{cmbright}\Huge\$ .