You may have correctly converted the angle to $\displaystyle{{315}}^{\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 sine is the y-coordinate. The correct answer is: $\displaystyle-\frac{\sqrt{{2}}}{{2}}\usepackage{cmbright}\Huge\$