Formule pentru semi-unghiuri ale funcțiilor trigonometrice:
[tex]$\sin({\frac{x}{2}}) = \sqrt{\frac{1 - \cos(x)}{2}}, x \in [0,\pi)$[/tex]
[tex]$\cos(\frac{x}{2}) = \sqrt{\frac{\cos(x) + 1}{2}}, x \in (-\frac{\pi}{2}, \frac{\pi}{2}]$[/tex]
[tex]$\cos(\frac{\pi}{12}) = \sqrt{\frac{1 + \cos(\frac{\pi}{6})}{2}} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2}}{2}} = \boxed{\frac{\sqrt{2 + \sqrt{3}}}{2}}$[/tex]
[tex]$\sin(\frac{\pi}{8}) = \sqrt{\frac{1 - \cos(\frac{\pi}{4})}{2}} = \sqrt{\frac{1 - \frac{\sqrt{2}}{2}}{2}} = \sqrt{\frac{2 - \sqrt{2}}{4}} = \boxed{\frac{\sqrt{2 - \sqrt{2}}}{2}}$[/tex]
[tex]$\cos{\frac{\pi}{8}} = \boxed{\frac{\sqrt{2 + \sqrt{2}}}{2}}$[/tex]
