Question

Решите уровнение
$\sqrt{2}\. sin( \frac{x}{3 =} ) = 1$
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Answer 1

$\sqrt{2}sin(\frac{x}{3} ) =1$

$sin(\frac{x}{3} )=\frac{1}{\sqrt{2} } \\\\sin(\frac{x}{3} )=\frac{\sqrt{2} }{2} \\\\\frac{x}{3}=(-1)^narccos\frac{\sqrt{2} }{2} + \pi n\\\\\frac{x}{3} =(-1)^n\frac{\pi}{4} +\pi n\\\\x=(-1)^n\frac{3\pi }{4}+3\pi n$

Ответ: $x=(-1)^n\frac{3\pi }{4}+3\pi n$, n ∈ Z