Question

решить уравнения тригонометрия (100баллов)

Answer 1

Ответ:

1.

$arccos( - \frac{ \sqrt{3} }{2} ) = \frac{5\pi}{6}$

2.

$arccos( \frac{ \sqrt{2} }{2} ) = \frac{\pi}{4}$

3.

$arccos( \frac{1}{2} ) = \frac{\pi}{3}$

4.

$arccos(0) = \frac{\pi}{2}$

5.

$arccos(1) = 0$

6.

$arccos( - \frac{ \sqrt{2} }{2} ) = \frac{3\pi}{4}$

7.

$arccos(0) + 3arccos(1) = \frac{\pi}{2} + 0 = \frac{\pi}{2}$

8.

$3arccos( - 1) - 2arccos(0) = 3\pi - 2 \times \frac{\pi}{2} = 2\pi$

9.

$12arccos( \frac{ \sqrt{3} }{2} ) - arccos( \frac{1}{2} ) = 12 \times \frac{\pi}{6} - \frac{\pi}{3} = \\ = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}$

10.

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

11.

$\cos(x) = \frac{ \sqrt{3} }{2} \\ x = + - \frac{\pi}{6} + 2 \pi \: n$

12.

$\cos(x) = - \frac{ \sqrt{2} }{2} \\ x = + - \frac{3\pi}{4} + 2\pi \: n$

13.

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

14.

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

15.

$\cos(x) = \frac{3}{4} \\ x = + - arccos( \frac{3}{4} ) + 2\pi \: n$

16.

$\cos(x) = - 0.3 \\ x = \pi + - arccos(0.3) + 2\pi \: n$

17.

$\cos(x) = - 0.2 \\ x = \pi+ - arccos(0.2) + 2\pi \: n$

18.

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

19.

$\cos(x) = \frac{4}{3}$

нет корней, так как

$- 1 \leqslant \cos(x) \leqslant 1$

везде n принадлежит Z.