Question

Calcule o cosseno de Pi/8

Answer 1

Veja que π/8 é a metade de π/4

A fórmula para o cosseno do arco metade é:

$cos(\frac{x}{2})=\pm \sqrt{\frac{1+cosx}{2}}\\ \\ cos(\frac{\pi}{8})=\pm\sqrt{\frac{1+\frac{\sqrt2}{2}}{2}}=\pm \sqrt{\frac{\frac{2+\sqrt2}{2}}{2}}=\pm\sqrt{\frac{2+\sqrt2}{4}}=\frac{2+\sqrt2}{2}$