Lista de exercícios do ensino médio para impressão
Resolver as equações:
a)
$\phantom{X}tg\,x\,=\,tg\,\dfrac{\,\pi\,}{5}\phantom{X}$
b)
$\phantom{X}cotg\,x\,=\,cotg\,\dfrac{\,5\pi\,}{6}\phantom{X}$
c)
$\phantom{X}3\,\centerdot\,tg\,x\,=\,\sqrt{\,3\,}\phantom{X}$
d)
$\phantom{X}cotg\,x\,=\,0\phantom{X}$
e)
$\phantom{X}cotg\,x\,=\,-1\phantom{X}$
f)
$\phantom{X}tg\,3x\,-\,tg\,2x\,=\,0\phantom{X}$
g)
$\phantom{X}tg\,2x\,=\,tg\,(x\,+\,\dfrac{\pi}{4})\phantom{X}$
h)
$\phantom{X}tg\,4x\,=\,1\phantom{X}$
i)
$\phantom{X}cotg\,2x\,=\,cotg(x\,+\,\dfrac{\pi}{4})\phantom{X}$
j)
$\phantom{X}tg^2\,2x\,=\,3\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{5}\,+\,k\pi\,\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{5\pi}{6}\,+\,k\pi\;\rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{6}\,+\,k\pi\;\rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{2}\,+\,k\pi\;\rbrace\,$
e) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{3\pi}{4}\,+\,k\pi\;\rbrace\,$
f) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,k\pi\;\rbrace\,$
g) $\,S\,=\,\varnothing\; \Leftarrow$
h) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{16}\,+\,\frac{k\pi}{4}\;\rbrace\,$
i) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\;\rbrace\,$
j) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{6}\,+\,\dfrac{k\pi}{2}\;$ ou $\phantom{X}x = \frac{\pi}{3} + \frac{k\pi}{2}\rbrace\,$

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Veja exercÍcio sobre:
trigonometria
equações trigonométricas