You may have miscalculated the effect of the $\displaystyle+\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ on the graph of sine. It will shift the graph of $\displaystyle{y}={\sin{\theta}}\usepackage{cmbright}\Huge\$ to the left by $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ units. 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.

So the graph of $\displaystyle{y}={\sin{{\left(\theta+\frac{\pi}{{2}}\right)}}}\usepackage{cmbright}\Huge\$ will have a hill with the y-axis running through the center of it. It will look like a cosine graph. This does not match the given graph.