You may have correctly determined that the reference angle is $\displaystyle{{45}}^{\circ}\usepackage{cmbright}\Huge\$ and then confused sine with tangent. To find the correct value of $\displaystyle{{\sin{{315}}}}^{\circ}\usepackage{cmbright}\Huge\$ , you must find the value of $\displaystyle{{\sin{{45}}}}^{\circ}\usepackage{cmbright}\Huge\$ and then determine the correct sign. To determine the correct sign, use the signs of x and y in the fourth quadrant, remembering that: $\displaystyle{\sin{\theta}}=\frac{{y}}{{1}}\usepackage{cmbright}\Huge\$