Answer
False.
$cos\frac{θ}{2}\gt0$
Work Step by Step
If $\frac{\pi}{2}\ltθ\lt\pi$, then $\frac{\pi}{4}\lt\frac{θ}{2}\lt\frac{\pi}{2}$. That is, $\frac{θ}{2}$ is in the Quadrant I. So:
$cos\frac{θ}{2}\gt0$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.