Question

Срочнооооооооо45 баллов

Answer 1

Ответ:

$\sin(5x + \frac{\pi}{4} ) = 1 \\ 5x + \frac{\pi}{4} = \frac{\pi}{2} + 2 \pi \: n \\ 5x = \frac{\pi}{4} + 2\pi \: n \\ x = \frac{\pi}{20} + \frac{2\pi \: n}{5}$

на интервале:

$- \frac{\pi}{2} < \frac{\pi}{20} + \frac{2\pi \: n}{5} < \frac{\pi}{2} \\ - 10 < 1 + 8n < 10 \\ - 11 < 8n < 9 \\ - \frac{11}{8} < n < \frac{9}{8} \\ - 1 \frac{3}{8} < n < 1 \frac{1}{8}$

n ∈{ -1; 0; 1}

Находим корни:

$x1 = \frac{\pi}{20} - \frac{2\pi}{5} = - \frac{7\pi}{20} \\ x2 = \frac{\pi}{20} + 0 = \frac{\pi}{20} \\ x3 = \frac{\pi}{20} + \frac{2\pi}{5} = \frac{9\pi}{20}$

сумма:

$-\frac{7\pi}{20} + \frac{\pi}{20} + \frac{9\pi}{20} = \frac{3\pi}{20}$

Ответ: 3П/20