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Explicação passo a passo:
[tex]sen(x+\frac{\pi }{3})=-\frac{\sqrt{2} }{2}[/tex]
[tex]sen(x+\frac{\pi }{3})=sen\frac{5\pi }{4} \\\\x+\frac{\pi }{3}=\frac{5\pi }{4}+2k\pi \\\\x=\frac{5\pi }{4} -\frac{\pi }{3}+2k\pi \\\\x=\frac{15\pi-4\pi }{12} +2k\pi \\\\x=\frac{11\pi }{12} +2k\pi , k \in~Z\\\\ou\\\\x+\frac{\pi }{3}=\frac{7\pi }{4}+2k\pi \\\\x=\frac{7\pi }{4}-\frac{\pi }{3} +2k\pi \\\\x=\frac{21\pi-4\pi }{12}+2k\pi \\\\x=\frac{17\pi }{4} +2k\pi ,~k~\in~Z[/tex]
