Lista de exercícios do ensino médio para impressão
Resolver as equações:
a)
$\phantom{X}sen\,x\,\,-\,\sqrt{\,3\,}\,\centerdot\,cosx\,=\,0\phantom{X}$
b)
$\phantom{X}sen^2\,x\,=\,cos^2\,x\phantom{X}$
c)
$\phantom{X}tg\,x\,+\,cotg\,x\,=\,2\phantom{X}$
d)
$\phantom{X}sec^2\,x\,=\,1\;+\;tg\,x\,\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{3}\,+\,k\pi\,\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\;ou\;x\,=\,\frac{3\pi}{4}\,+\,k\pi;\rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\,\rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,k\pi\;ou\;x\,=\,\frac{\pi}{4}\,+\,k\pi\;\rbrace\,$

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Resolver as equações:
a)
$\phantom{X}tg\,x\,=\,1\phantom{X}$
b)
$\phantom{X}cotg\,x\,=\,\sqrt{\,3\,}\phantom{X}$
c)
$\phantom{X}tg\,x\,=\,-\sqrt{\,3\,}\phantom{X}$
d)
$\phantom{X}tg\,x\,=\,0\phantom{X}$
f)
$\phantom{X}tg\,2x\,=\,\sqrt{\,3\,}\phantom{X}$
g)
$\phantom{X}tg\,2x\,=\,tg\,x\phantom{X}$
h)
$\phantom{X}tg\,3x\,=\,1\phantom{X}$
i)
$\phantom{X}tg\,5x\,=\,tg\,3x\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\,\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{6}\,+\,k\pi\,\rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{2\pi}{3}\,+\,k\pi\,\rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,k\pi\,\rbrace\,$
e) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{6}\,+\,\frac{k\pi}{2}\,\rbrace\,$
f) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,k\pi\,\rbrace\;$
g) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{12}\,+\,\frac{k\pi}{3}\,\rbrace\,$
h) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{k\pi}{2}, k é par\,\rbrace\,$

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Veja exercÍcio sobre:
trigonometria
equações trigonométricas