Answer
$positive$, $I$, $30^\circ$, $\frac{\sqrt 3}{2}$.
Work Step by Step
We can identify $\theta=390^\circ$ to be in quadrant $I$, thus $cos\theta$ will be $positive$. The reference angle is the acute angle formed by the terminal line with x-axis and it can be found as $390^\circ-360^\circ=30^\circ$, thus the exact value is $cos390^\circ=cos30^\circ=\frac{\sqrt 3}{2}$.
The answers are $positive$, $I$, $30^\circ$, $\frac{\sqrt 3}{2}$.
