Answer
$\frac{2\sqrt 3}{3}$
Work Step by Step
To find exact value of $\sec (-330)^{\circ}$, let's find its reference angle first. As $ (-330)^{\circ}$ terminates in quadrant I,
The reference angle = $ 360^{\circ} - 330^{\circ} $ = $30^{\circ}$
As $ (-330)^{\circ}$ terminates in quadrant I, its $\sec$ will be positive. Therefore by reference angle theorem-
$\sec (-330)^{\circ}$ = $\sec 30^{\circ}$
= $\frac{2}{\sqrt 3}$ = $\frac{2\sqrt 3}{3}$
