Bisection formulae

By inverting the cosine duplication formulae we obtain the bisection formulae, which express $\sin(\alpha/2)$ and $\cos(\alpha/2)$ in terms of $\cos\alpha$ alone. A double sign $\pm$ appears, to be chosen according to the quadrant in which $\alpha/2$ falls.

• The bisection formulae
• Proof of the bisection formulae
• Example: cosine of 15°