Question

с тригонометрическими уравнениями дам 100

Answer 1

18.

$tg( \frac{\pi(x + 8)}{6} ) = - \frac{1}{ \sqrt{3} } \\ \frac{\pi(x + 8)}{6} = - \frac{\pi}{6} + \pi \: n \: \: \: | \times \frac{6}{\pi} \\ x + 8 = - 1 + 6n \\ x = - 9 + 6n$

$n1 = - 1 \\ x1 = - 15 \\ \\ n2 = 0 \\ x2 = - 9 \\ \\ n3 = 1 \\ x3 = - 3 \\ \\ n4 = 2 \\ x4 = 3$

ответ: -3

19.

$tg( \frac{\pi(2x + 1)}{6} ) = \frac{1}{ \sqrt{3} } \\ \frac{\pi(2x + 1)}{6} = \frac{ \pi}{6} + \pi \: n \: \: \: | \times \frac{6}{\pi} \\ 2x + 1 = 1 + 6n \\ 2x = 6n \\ x = 3n$

наибольший отрицательный при n = -1

x = -3

ответ: -3

20.

$tg( \frac{\pi(2x + 1)}{3} ) = - \sqrt{3} \\ \frac{\pi(2x + 1)}{3} = - \frac{\pi}{3} + \pi \: n \: \: \: | \times \frac{3}{\pi} \\ 2x + 1 = - 1 + 3n \\ 2x = - 2 + 3n \\ x = - 1 + \frac{3n}{2} \\ x = - 1 + 1.5n$

$n1 = - 1 \\ x1 = - 2.5 \\ \\ n2 = 0 \\ x2 = - 1 \\ \\ n 3 = 1 \\ x3 = 0.5$

ответ: -1