Perhaps you chose this answer because you knew you had to divide something by the coefficient of x, which in this case is 4. However, the period of $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ is given by $\displaystyle\frac{{{2}\pi}}{{\left|{b}\right|}}\usepackage{cmbright}\Huge\$ .