Half Angle Identity

Derived from the Reduction Identity which was also derived from the Double Angle Identity

used if you have a trigonometric function where you have half of a Unit Circle angle

$\sin (\frac{x}{2})=\pm \sqrt{\frac{1-\cos x}{2}}$ $\cos (\frac{x}{2})=\pm \sqrt{\frac{1+\cos x}{2}}$ $\tan (\frac{x}{2})=\pm \sqrt{\frac{1-\cos x}{1+\cos x}}$

Note that these identities are in $\pm$ form. You will have to manually determine which quadrant the angle is in, and validate these sine values. You cannot have 2 sine values, find which one is the fake.