Решение.
Тригонометрическое неравенство .
[tex]\bf sin3x < \dfrac{1}{2}\ \ \ \Rightarrow \ \ \ \ \dfrac{5\pi }{6}+2\pi n < 3x < 2\pi +\dfrac{\pi }{6}+2\pi n\ \ ,\ n\in Z\\\\\\\dfrac{5\pi }{6}+2\pi n < 3x < \dfrac{13\pi }{6}+2\pi n\ \ ,\ n\in Z\\\\\\\dfrac{5\pi }{18}+\dfrac{2\pi n}{3} < x < \dfrac{13\pi }{18}+\dfrac{2\pi n}{3}\ \ ,\ n\in Z[/tex]
Ответ: [tex]\bf x\in \Big(\, \dfrac{5\pi }{18}+\dfrac{2\pi n}{3}\ ;\ \dfrac{13\pi }{18}+\dfrac{2\pi n}{3}\ \Big )\ \ ,\ n\in Z[/tex] .
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Решение.
Тригонометрическое неравенство .
[tex]\bf sin3x < \dfrac{1}{2}\ \ \ \Rightarrow \ \ \ \ \dfrac{5\pi }{6}+2\pi n < 3x < 2\pi +\dfrac{\pi }{6}+2\pi n\ \ ,\ n\in Z\\\\\\\dfrac{5\pi }{6}+2\pi n < 3x < \dfrac{13\pi }{6}+2\pi n\ \ ,\ n\in Z\\\\\\\dfrac{5\pi }{18}+\dfrac{2\pi n}{3} < x < \dfrac{13\pi }{18}+\dfrac{2\pi n}{3}\ \ ,\ n\in Z[/tex]
Ответ: [tex]\bf x\in \Big(\, \dfrac{5\pi }{18}+\dfrac{2\pi n}{3}\ ;\ \dfrac{13\pi }{18}+\dfrac{2\pi n}{3}\ \Big )\ \ ,\ n\in Z[/tex] .