Question

2) Решите уравнение.

Answer 1

$\sin( \frac{\pi(2x - 3)}{6} ) = - \frac{1}{2}$

Возможны 2 случая:

1.

$\frac{\pi(2x - 3)}{6} = \frac{7\pi}{6} + 2\pi n \\ \pi(2x - 3) = 7\pi + 12\pi n \\ 2x - 3 = 7 + 12n \\ 2x = 10 + 12n \\ x = 5 + 6n$

2.

$\frac{\pi(2x - 3)}{6} = \frac{11\pi}{6} + 2\pi n \\ \pi(2x - 3) = 11\pi + 12\pi n \\ 2x - 3 = 11 + 12n \\ 2x = 14 + 12n \\ x = 7 + 6n$

Ответ:

$x_{1} = 5 + 6n, nєZ \\ x_{2} = 7 + 6n, nєZ$