You may have correctly determined that the reference angle is $\displaystyle{{30}}^{\circ}\usepackage{cmbright}\Huge\$ and then confused secant with cosecant. To find the correct value of $\displaystyle{{\sec{{150}}}}^{\circ}\usepackage{cmbright}\Huge\$ , you must find the value of $\displaystyle{{\sec{{30}}}}^{\circ}\usepackage{cmbright}\Huge\$ and then determine the correct sign. To determine the sign, use the signs of x and y in the second quadrant, remembering that: $\displaystyle{\sec{\theta}}=\frac{{1}}{{x}}\usepackage{cmbright}\Huge\$