Draw $\displaystyle{{120}}^{\circ}\usepackage{cmbright}\Huge\$ in standard position. The terminal side is in the second quadrant and the reference angle is $\displaystyle{{60}}^{\circ}\usepackage{cmbright}\Huge\$ . Use the $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle to find the value of this function at the reference angle:

$\displaystyle{{\sec{{60}}}}^{\circ}=\frac{{2}}{{1}}={2}\usepackage{cmbright}\Huge\$

Use the signs of x and y in the second quadrant to determine the sign of secant:

$\displaystyle{{\sec{{120}}}}^{\circ}=\frac{{1}}{{x}}=\frac{{{\left(+\right)}}}{{{\left(-\right)}}}={\left(-\right)}\usepackage{cmbright}\Huge\$

So $\displaystyle{{\sec{{120}}}}^{\circ}=-{2}\usepackage{cmbright}\Huge\$ .