You may have correctly determined that the reference angle is $\displaystyle{{60}}^{\circ}\usepackage{cmbright}\Huge\$ and then confused sine with cosine. To find the correct value of $\displaystyle{{\sin{{240}}}}^{\circ}\usepackage{cmbright}\Huge\$ you must find the value of $\displaystyle{{\sin{{60}}}}^{\circ}\usepackage{cmbright}\Huge\$ and then determine the correct sign. To determine the correct sign, use the signs of x and y in the third quadrant, remembering that: $\displaystyle{\sin{\theta}}=\frac{{y}}{{1}}\usepackage{cmbright}\Huge\$