Question

решите уравнения
хотяб 4-5 шт

Answer 1

Ответ:

1

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

2

$\cos( \frac{x}{2} ) = - 1 \\ \frac{x}{2} = \pi + 2\pi \: n \\ x = 2\pi + 4\pi \: n$

3

$tg3x = 1 \\ 3x = \frac{\pi}{4} + \pi \: n \\ x = \frac{\pi}{12} + \frac{\pi \: n}{3}$

4

$tg2x = \sqrt{3} \\ 2x = \frac{\pi}{3} + \pi \: n \\ x = \frac{\pi}{6} + \frac{\pi \: n}{2}$

5

$\sin(2x) = \frac{1}{2} \\ \\ 2x = \frac{\pi}{6} + 2\pi \: n \\ x_1 \frac{\pi}{12} + \pi \: n \\ \\ 2x = \frac{5\pi}{6} + 2\pi \: n \\ x_2 = \frac{5\pi}{12} + \pi \: n$

6

$2 \cos {}^{2} (x) - 5 \cos(x) + 2 = 0 \\ \\ \cos(x) = t \\ \\ 2t {}^{2} - 5 t + 2 = 0\\ D = 25 - 16 = 9 \\ t_1 = \frac{5 + 3}{4} = 2 \\ t_2 = 0.5 \\ \\ \cos(x) = 2$

нет корней

$\cos(x) = 0.5 \\ x = \pm \frac{\pi}{3} + 2\pi \: n$

везде n принадлежит Z