You may have correctly converted the angle to $\displaystyle{{135}}^{\circ}\usepackage{cmbright}\Huge\$ and found that it intersects the unit circle at the point $\displaystyle{\left(-\frac{\sqrt{{2}}}{{2}},\frac{\sqrt{{2}}}{{2}}\right)}\usepackage{cmbright}\Huge\$ . However, the value of cosine is the x-coordinate.