The period of $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ equals $\displaystyle\frac{{{2}\pi}}{{\left|{b}\right|}}\usepackage{cmbright}\Huge\$ . So the period of $\displaystyle{y}={3}{\cos{\pi}}{x}\usepackage{cmbright}\Huge\$ is:

$\displaystyle\frac{{{2}\pi}}{{\left|\pi\right|}}=\frac{{{2}\pi}}{\pi}={2}\usepackage{cmbright}\Huge\$