Exercício sobre trigonometria

Resolver em $\,{\rm I\!R}\,$ as seguintes equações:

$\,sen^2\,x\,=\,\dfrac{\;1\;}{\;4\;}\,$

$\,sen^2\,x\;-\;sen\,x\;=\;0\,$

$\,2\,\centerdot\,sen^2\,x\,-\,3\,\centerdot\,sen\,x\,+\,1\,=\,0\,$

$\,2\,\centerdot\,cos^2\,x\,=\,1\,-\,sen\,x\,$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{6}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{5\pi}{6}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{7\pi}{6}\,+\,2k\pi\;$ ou $\,x\,=\,- \frac{\pi}{6}\,+\,2k\pi\,\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,k\,\pi\;$ ou $\,x\,=\,\frac{\pi}{2}\,+\,2k\pi\,\rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{2}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{\pi}{6}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{5\pi}{6}\,+\,2k\pi\,\rbrace\,$
d)$\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{2}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{-\pi}{6}\,+\,2k\pi\;$ ou $\,x\,=\,\frac{7\pi}{6}\,+\,2k\pi\,\rbrace\,$

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