Arco metade.

Vamos partir de uma simples fórmula que pode ser escrita de duas formas:

$\cos 2\alpha = 2\cos^2 \alpha - 1 = 1 - 2\sin^2 \alpha$.

Tomando $\theta = 2\alpha$:

$\cos \theta = 2\cos^2 \dfrac{\theta}{2} - 1\ \Rightarrow\ \fbox{$\cos \dfrac{\theta}{2} = \pm \sqrt{\dfrac{\cos \theta + 1}{2}}$}$;

$\cos \theta = 1 - 2\sin^2 \dfrac{\theta}{2}\ \Rightarrow\ \fbox{$\sin \dfrac{\theta}{2} = \pm \sqrt{\dfrac{1 - \cos \theta}{2}}$}$;

$\fbox{$\tan \dfrac{\theta}{2} = \pm \sqrt{\dfrac{1 - \cos \theta}{1 + \cos \theta}}$}$; $\fbox{$\cot \dfrac{\theta}{2} = \pm \sqrt{\dfrac{1 + \cos \theta}{1 - \cos \theta}}$}$;

$\fbox{$\sec \dfrac{\theta}{2} = \pm \sqrt{\dfrac{2}{\cos \theta + 1}}$}$; $\fbox{$\csc \dfrac{\theta}{2} = \pm \sqrt{\dfrac{2}{1 - \cos \theta}}$}$;

$\fbox{$cord\ \dfrac{\theta}{2} = \sqrt{2\left(1 \pm \sqrt{\dfrac{1 + \cos \theta}{2}}\right)}$}$.