If you shift the graph of $\displaystyle{y}={\cos{\theta}}\usepackage{cmbright}\Huge\$ by $\displaystyle\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ units to the left, the hill that had the y-axis running through the center will now be positioned on the interval $\displaystyle{\left[-\pi,{0}\right]}\usepackage{cmbright}\Huge\$ . But the graph of $\displaystyle{y}={\sin{\theta}}\usepackage{cmbright}\Huge\$ has a valley on that interval, so they are not the same graph.