You may have correctly determined that the reference angle is $\displaystyle{{45}}^{\circ}\usepackage{cmbright}\Huge\$ and then confused tangent with sine. To find the correct value of $\displaystyle{{\tan{{135}}}}^{\circ}\usepackage{cmbright}\Huge\$ you must find the value of $\displaystyle{{\tan{{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 second quadrant, remembering that

$\displaystyle{\tan{\theta}}=\frac{{y}}{{x}}\usepackage{cmbright}\Huge\$ . The correct answer is $\displaystyle-{1}\usepackage{cmbright}\Huge\$ .