Question

qual o seno de -5pi:6 ??

Answer 1

Utilizaremos estas propriedades:

$\begin{array}{rcrc} \mathrm{sen}\left(-x \right )&=&-\mathrm{sen}\left(x \right )&\;\;(i)\\ \mathrm{sen}\left(\pi-x \right )&=&\mathrm{sen}\left(x \right )&\;\;(ii) \end{array}$


Então para $x=\frac{5\pi}{6}$, temos

$\mathrm{sen}\left(-\frac{5\pi}{6} \right )\\ \\ =-\mathrm{sen}\left(\frac{5\pi}{6} \right )\\ \\=-\mathrm{sen}\left(\pi-\frac{5\pi}{6} \right )\\ \\ =-\mathrm{sen}\left(\frac{6\pi-5\pi}{6} \right )\\ \\ =-\mathrm{sen}\left(\frac{\pi}{6} \right )\\ \\ =-\frac{1}{2} \Rightarrow \boxed{\mathrm{sen}\left(-\frac{5\pi}{6}\right)=-\frac{1}{2}\\ \\}}$