Exercício sobre trigonometria

Resolver em $\,{\rm I\!R}\,$ a equação $\phantom{X}sen\,x\;=\;sen\,\dfrac{\;\pi\;}{\;5\;}\phantom{X}$

resposta:

ciclo trigonométrico senx igual sen pi sobre 5

1. x pode ser:
$\,x\,=\,\dfrac{\,\pi\,}{5}\,+\,2k\pi,\,k\,\in\,\mathbb{Z}\,$ ou
2. x pode ser também:
$\,x\,=\,\left(\pi\,-\,\dfrac{\,\pi\,}{5}\right)\,+\,2k\pi\,=\,$$\dfrac{\,4\pi\,}{5}\,+\,2k\pi,\,k\,\in\,\mathbb{Z}\,$

$\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\,|\,x\,=\,\frac{\pi}{5}\,+\,2k\pi\,$ $\,{\text ou}\,x\,=\,\frac{4\pi}{5}\,+\,2k\pi,\phantom{X}k\,\in\,\mathbb{Z}\rbrace\,$
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