Half Angle Formulas/Sine/Proof 2

Proof
Define:


 * $u = \dfrac \theta 2$

Then:

We also have that:
 * In quadrant $\text I$, and quadrant $\text {II}$, $\sin \theta > 0$
 * In quadrant $\text {III}$, and quadrant $\text {IV}$, $\sin \theta < 0$.