You seem to have confused the roles of a and b. The amplitude of $\displaystyle{y}={2}{\sin{{4}}}{x}\usepackage{cmbright}\Huge\$ is 2, while the amplitude of the graph is 4. The period of $\displaystyle{y}={2}{\sin{{4}}}{x}\usepackage{cmbright}\Huge\$ is $\displaystyle\frac{{\pi}}{{2}}\usepackage{cmbright}\Huge\$ , while the period of the function in the graph is $\displaystyle\pi\usepackage{cmbright}\Huge\$ .