Exercício sobre trigonometria

Resolver as equações:

$\phantom{X}4 \centerdot cos^2 x = 3\phantom{X}$

$\phantom{X}cos^2\,x\,+\,cos\,x\,=\,0\phantom{X}$

$\phantom{X}sen^2\,x\,=\,1\,+\,cos\,x\phantom{X}$

$\phantom{X}cos\,2x\,+\,3\,\centerdot\,cos\,x\,+\,2\,=\,0\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{\pi}{6}\,+\,2k\pi \, ou \, x\,=\,\pm\,\frac{5\pi}{6}\,+\,2k\pi\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\frac{\pi}{2}\,+\,k\pi\;ou\;x\,=\,\pi\,+\,2k\pi \, \rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\frac{\pi}{2}\,+\,k\pi\;ou\;x\,=\,\pi\,+\,2k\pi \, \rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pi + 2k\pi \; ou \; x\,=\,\pm\,\frac{2\pi}{3}\,+\,2k\pi \rbrace\,$

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