Answer
False.
$sin\frac{u}{2}=+\sqrt {\frac{1-cos~u}{2}}$
Work Step by Step
If $u$ is in the second quadrant: $\frac{\pi}{2}\lt u\lt\pi$. Then, $\frac{\pi}{4}\lt \frac{u}{2}\lt\frac{\pi}{2}$. That is $u$ is in the first quadrant. So,
$sin\frac{u}{2}\gt0$
