You may have thought that the effect of subtracting a constant from the input was to shift the graph of the original function to the left, but actually it will shift to the right. So the graph of $\displaystyle{y}={\cos{{\left(\theta-\frac{\pi}{{2}}\right)}}}\usepackage{cmbright}\Huge\$ will be the same as the graph of sine, which is not the graph shown.