Answer
Exact value of $\sec 120^{\circ}= -2$
Work Step by Step
To find exact value of $\sec 120^{\circ}$, let's find its reference angle first. As $ 120^{\circ}$ terminates in quadrant II,
The reference angle = $ 180^{\circ} - 120^{\circ}$ = $60^{\circ}$
As $ 120^{\circ}$ terminates in quadrant II, its $\sec$ will be negative. Therefore by reference angle theorem-
$\sec 120^{\circ}$ = $-\sec 60^{\circ}$
= -2
