You may have miscalculated the effect of subtracting $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ from the input of the function. It will 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 with they y-axis 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\$ . This does not match the given graph.