Question

sin (1/2 x -pi/6) =1/2
Помогите пожалуйста

Answer 1

Решение:

$sin(\frac{1}{2}x-\frac{\pi}{6}) = \frac{1}{2}\\ \frac{1}{2}x-\frac{\pi}{6} = (-1)^{n}*arcsin\frac{1}{2}+\pi n\\ \frac{1}{2}x-\frac{\pi}{6} = (-1)^{n}*\frac{\pi}{6}+\pi n\\ \frac{1}{2}x = (-1)^{n}*\frac{\pi}{6}+\frac{\pi}{6}+\pi n|*6\\3x = (-1)^{n}*\pi+\pi + 6\pi n\\x = (-1)*\pi+\pi*\frac{1}{3}+6\pi n*\frac{1}{3}\\x = \frac{(-1)^{n}*\pi +\pi}{3}+2\pi n$n∈Z

Ответ: $x = \frac{(-1)^{n}*\pi +\pi }{3}+2\pi n$, n∈Z