Half Angle Formulas/Sine/Proof 2

Theorem
where $\sin$ denotes sine and $\cos$ denotes cosine.

Proof
Define:


 * $u = \dfrac \theta 2$

Then:

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