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