It looks like you confused the effect of a and b in $\displaystyle{y}={a}{\sin{{b}}}{x}\usepackage{cmbright}\Huge\$ . The amplitude of this graph is 2, while the amplitude of $\displaystyle{y}={3}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ is 3. This graph has 3 cycles in the interval $\displaystyle{\left[{0},{2}\pi\right]}\usepackage{cmbright}\Huge\$ , or a period of $\displaystyle\frac{{{2}\pi}}{{3}}\usepackage{cmbright}\Huge\$ . The period of $\displaystyle{y}={3}{\sin{{2}}}{x}\usepackage{cmbright}\Huge\$ is $\displaystyle\pi\usepackage{cmbright}\Huge\$ .