Answer
$sin$$\frac{\theta}{2}$ is positive in the interval (90$^{\circ}$,180$^{\circ}$).
Work Step by Step
$\theta$ is in the interval (90$^{\circ}$,180$^{\circ}$)
Therefore: $\frac{\theta}{2}$ $\leq$ 90$^{\circ}$
Therefore, $\frac{\theta}{2}$ exists in Quadrant 1.
All trigonometric functions are positive in Quadrant 1. Therefore $sin$$\frac{\theta}{2}$ is positive in the interval (90$^{\circ}$,180$^{\circ}$).
