Question

помогите пожалуйста даю 20 баллов​

Answer 1

$arcsin(0) = 0 \\ arcsin( - \frac{ \sqrt{2} }{2} ) = \frac{7\pi}{4} \\ arccos( - 1) = \pi \\ arctg(1) = \frac{\pi}{4} \\ arccos(0) = \frac{\pi}{2}$

$arccos( \frac{ \sqrt{3} }{2} ) = \frac{\pi}{6}$

$arctg( \sqrt{3} ) = \frac{\pi}{3} \\ arcsin( \frac{1}{2} ) = \frac{\pi}{6} \\ arccos( - \frac{1}{2} ) = \frac{2\pi}{3} \\ arctg( \frac{ \sqrt{ 3} }{3} ) = \frac{\pi}{6}$

2.

$\cos(2x) = \frac{ \sqrt{3} }{3} \\ 2x = \pm \: arccos( \frac{ \sqrt{3} }{3} ) + 2\pi \: n \\ x = \pm \frac{1}{2} arccos( \frac{ \sqrt{3} }{3} ) + \pi \: n$

n принадлежит Z.

3 .

$2 \cos {}^{2} (x) + 9 \sin(x) + 3 = 0 \\ 2 - 2 \sin {}^{2} (x) + 9 \sin(x) + 3 = 0 \\ 2 \sin {}^{2} (x) - 9\sin(x) - 5 = 0 \\ \\ \sin( x) = t \\ \\ 2 {t}^{2} - 9t - 5 = 0 \\ D = 81 + 40 = 121 \\ t_1 = \frac{9 + 11}{4} = 5 \\ t_2 = - \frac{1}{2} \\ \\ \sin(x) = 5 \\ \text{нет корней} \\ \\ \sin(x) = - \frac{1}{2} \\ x_1 = - \frac{\pi}{6} + 2 \pi \: n \\ x_2 = - \frac{5\pi}{6} + 2\pi \: n$