HALF ANGLE FORMULAE

Half Angle Formulae

Sometimes it is convenient to use half angle formulae for the solution of oblique triangles when measures of three sides of a triangle are given. In this section, we will study half angles formulae for sines, cosines and tangents. Let us derive them one by one.

(a) Cosines of Half Angle

Statement: In any triangle ABC with usual notations,

\cos \frac{α}{2} = \sqrt{\frac{S (S - a)}{b c}}, \cos \frac{β}{2} = \sqrt{\frac{S (S - b)}{a c}}, \cos \frac{γ}{2} = \sqrt{\frac{S (S - c)}{a b}}

(a) Cosines of Half Angle

(b) Sines of Half Angle