The effect of subtracting $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ from the input of the function is to shift the graph of $\displaystyle{y}={\sin{\theta}}\usepackage{cmbright}\Huge\$ to the right by $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ units. So, for example, the valley that was on the interval $\displaystyle{\left[-\pi,{0}\right]}\usepackage{cmbright}\Huge\$ in the graph of $\displaystyle{y}={\sin{\theta}}\usepackage{cmbright}\Huge\$ becomes a valley with the y-axis running through the center in the graph of $\displaystyle{y}={\sin{{\left(\theta-\frac{\pi}{{2}}\right)}}}\usepackage{cmbright}\Huge\$ . The hill and valley pattern repeats on both sides and this is a description of the graph shown.