Question

Cos(4x-30°)=1/3

sin(x+π/3)=1/2

tg(2x+15°)=кореньиз2/2

Answer 1

1.

$\cos(4x - 30°) = \frac{1}{3} \\ \\ 4x 1- 30 °= arccos( \frac{1}{3} ) + 2\pi \: n \\ 4x1 = 30 °+ arccos( \frac{1}{3} ) + 2\pi \: n \\ x1 = 7.5° + \frac{1}{4}arccos( \frac{1}{3} ) + \frac{\pi \: n}{2} \\ \\ 4x2 - 30 °= - arccos( \frac{1}{3} ) + 2\pi \: n \\ x2 =7 .5 °- \frac{1}{4} arccos( \frac{1}{3} ) + \frac{\pi \: n}{2}$

n принадлежит Z.

2.

$\sin(x + \frac{\pi}{3} ) = \frac{1}{2} \\ \\ x1 + \frac{\pi}{3} = \frac{\pi}{6} + 2\pi\ \: n \\ x1 = - \frac{\pi}{6} + 2\pi \: n \\ \\ x2 + \frac{\pi}{3} = \frac{5\pi}{6} + 2\pi \: n \\ x2 = \frac{\pi}{2} + 2\pi \: n$

n принадлежит Z.

3.

$tg(2x + 15°) = \frac{ \sqrt{2} }{2} \\ 2x + 15° = \frac{\pi}{4} + \pi \: n \\ 2x = - 15° + 45 °+ \pi \: n \\ 2x = 30° + \pi \: n \\ 2x = \frac{\pi}{6} + \pi \: n \\ x = \frac{\pi}{12} + \frac{\pi \: n}{2}$

n принадлежит Z.