Question

с математикой!
Решите 151-153 номера!
См.фото!

Answer 1

151.

1.

$\sin(x) = \frac{ \sqrt{2} }{2} \\ x1 = \frac{\pi}{4} + 2 \pi \: n \\ x2 = \frac{3\pi}{4} + 2\pi \: n$

2.

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

3.

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

3.

$ctg(x) = 2.05 \\ x = arcctg(2.05) + \pi \: n$

152.

1.

$\sin(x) = - \frac{ \sqrt{3} }{2} \\ x1 = - \frac{\pi}{3} + 2\pi \: n \\ x2 = - \frac{2\pi}{3} + 2 \pi \: n$

2.

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

3.

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

4.

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

153.

1.

$\sin(2x) = \frac{1}{2} \\2x1 = \frac{\pi}{6} + 2\pi \: n \\ x1 = \frac{\pi}{12} + \pi \: n \\ \\ 2x2 = \frac{5\pi}{ 6} + 2\pi \: n \\ x2 = \frac{5\pi}{12} + \pi \: n$

2.

$\cos(2x) = 1 \\ 2x = 2\pi \: n \\ x = \pi \: n$

3.

$\sin(x) = \frac{4}{5} \\ x = {( - 1)}^{n} arcsin( \frac{4}{5} ) + \pi \: n$

4.

$tg(3x) = \frac{ \sqrt{3} }{3} \\ 3x = \frac{\pi}{6} + \pi \: n \\ x = \frac{\pi}{18} + \frac{\pi \: n}{3}$

Везде n принадлежит z.