Question

Sin(3x + pi/3)=√2/2 Решите пожалуйста

Answer 1

Заменим

$3x + \frac{\pi}{3} = t \\ \sin \: t = \frac{ \sqrt{2} }{2} \\ t = \frac{\pi}{4} + 2\pi \: k \\ t = \frac{3\pi}{4} \: + 2\pi \: k$

Обратная замена

$3x + \frac{\pi}{3} = \frac{\pi}{4} + 2\pi \: k \\ 3x = \frac{\pi}{4} - \frac{\pi}{3} + 2\pi \: k = \frac{3\pi - 4\pi}{12} + 2\pi \: k = - \frac{\pi}{12} + 2\pi \: k \\ x = - \frac{\pi}{36} + \frac{2}{3} \pi \: k$

$3x + \frac{\pi}{3} = \frac{3\pi}{4} + 2\pi \: k \\ 3x = \frac{9\pi - 4\pi}{12} + 2\pi \: k \\ x = \frac{5\pi}{36} + 2\pi \: k$

К∈z, z-целое число