You may have thought that the effect of subtracting $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ from the input was to shift the graph of the original function to the left, but actually it will shift to the right. 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\$ , which is not the graph shown.