Exercício sobre trigonometria

Resolver as equações:

$\,cos\,x\,=\,cos\,\dfrac{\,\pi\,}{5}\,$

$\,sec\,x\,=\,sec\,\dfrac{\,2\pi\,}{3}\,$

$\,cos\,x\,=\,0\,$

$\,cos\,x\,=\,1\,$

$\,cos\,x\,=\,-1\,$

$\,cos\,x\,=\,\dfrac{\,1\,}{2}\,$

$\,cos\,x\,=\,\dfrac{\,\sqrt{\,2\,}\,}{2}\,$

$\,cos\,x\,=\,\dfrac{\,\sqrt{\,3\,}\,}{2}\,$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{\pi}{5}\,+\,2k\pi \, \rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{2\pi}{3}\,+\,2k\pi \, \rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{\pi}{2}\,+\,2k\pi \, \rbrace\, =\,$ $\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\frac{\pi}{2}\,+\,k\pi \, \rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,2k\pi \, \rbrace\,$
e) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pi\,+\,2k\pi \, \rbrace\,$
f) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{\pi}{3}\,+\,2k\pi \, \rbrace\,$
g) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{\pi}{4}\,+\,2k\pi \, \rbrace\,$
h) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{5\pi}{6}\,+\,2k\pi \, \rbrace\,$

×