You probably made a mistake with the calculation of the period. The amplitude of this graph and $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is 3. However, this graph has a period of $\displaystyle\pi\usepackage{cmbright}\Huge\$ , while $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ has a period of $\displaystyle{4}\pi\usepackage{cmbright}\Huge\$ . You should also pay attention to the negative sign in $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ . This will cause the graph to be a reflection of the graph of $\displaystyle{y}={3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ over the x-axis, making it so that there will be a valley occuring on the y-axis.