### Instruction: Find $\sec 120^\circ.$.### Response: To find the secant of an angle, I need to know the cosine of that angle, since $\sec \theta = \frac{1}{\cos \theta}.$
I can use the fact that $\cos 120^\circ = -\frac{1}{2},$ which I know from the unit circle or from the cosine subtraction formula.
Therefore, $\sec 120^\circ = \frac{1}{-\frac{1}{2}} = -2.$