Question

Даю 40 баллов Решите пожалуйста неравенство

Answer 1

$Sin(x-\frac{\pi }{4})\leq \frac{1}{2}\\\\-\pi-arcSin\frac{1}{2}+2\pi n \leq x -\frac{\pi }{4}\leq arcSin\frac{1}{2}+2\pi n \\\\-\pi-\frac{\pi }{6}+2\pi n  \leq x-\frac{\pi }{4}\leq\frac{\pi }{6}+2\pi n \\\\-\frac{7\pi }{6}+2\pi n\leq x-\frac{\pi }{4}\leq \frac{\pi }{6}+2\pi n\\\\-\frac{7\pi }{6}+\frac{\pi }{4}+2\pi n \leq x \leq\frac{\pi }{6}+\frac{\pi }{4}+2\pi n\\\\-\frac{11\pi }{12}+2\pi n\leq x \leq \frac{5\pi }{12}+2\pi n$

$Otvet:\boxed{ x\in[-\frac{11\pi }{12}+2\pi n;\frac{5\pi }{12}+2\pi n],n\in Z}$