Question

Resolva a expressão trigonométrica:

Answer 1

Primeiro convertemos as unidades
$\frac{\pi}{3} = 60\º \\ \frac{\pi}{6}= 30\° \\ cos30=\frac{\sqrt{3}}{2}\\ sen60=\frac{\sqrt{3}}{2}\\\\ \frac{2cos \frac{\pi}{6}-4sen\frac{\pi}{3}}{4cos \frac{\pi}{6} +8sen\frac{\pi}{3}}\\\\ (I) \ \ 2\frac{\sqrt{3}}{2}-4\frac{\sqrt{3}}{2}=-2\frac{\sqrt{3}}{2}\\ (II) \ \ 4\frac{\sqrt{3}}{2}+8\frac{\sqrt{3}}{2}=12\frac{\sqrt{3}}{2}\\\\ (I/II)=\\\\ \frac{-2\frac{\sqrt{3}}{2}}{12\frac{\sqrt{3}}{2}} \\ \frac{-1}{6}$

Resposta: $\frac{-1}{6}$