Answer
Positive.
Work Step by Step
$-90^{\circ}\lt\theta\lt 90^{\circ}\implies-45^{\circ}\lt\frac{\theta}{2}\lt 45^{\circ}$
Cosine function is positive as the angle $\frac{\theta}{2}$ is in between $-45^{\circ}$ and $45^{\circ}$( This interval is a part of first and fourth quadrants. In these quadrants, cosine function is positive ).
