Answer
Negative.
Work Step by Step
$270 < A < 360$
Dividing by 2
$135 < \dfrac{A}{2} < 180$
$\therefore \dfrac{A}{2} $ terminates in $QII$
$\because $ The cosine of an angle in $QII$ is negative
$\therefore \cos{\dfrac{A}{2}}$ is negative.