Question

ctg(2x/3)>√3/3
Даю 50 БАЛЛОВ

Answer 1

Ответ:

$ctg( \frac{2x}{3} ) > \frac{ \sqrt{3} }{3}$

рисунок

$\frac{2x}{3} \in(\pi \: n ;\frac{\pi}{3} + \pi \: n) \: \: \: | \times \frac{3}{2} \\ x\in( \frac{3\pi \: n}{2} ; \frac{\pi}{2} + \frac{3\pi \: n}{2} ) \\ n\in \: Z$

Answer 2

$Ctg(\frac{2x}{3})>\frac{\sqrt{3} }{3}\\\\\pi n<\frac{2x}{3} <arcCtg(\frac{\sqrt{3} }{3} )+\pi n,n\in Z\\\\\pi n<\frac{2x}{3} < \frac{\pi }{3}+\pi n,n\in Z\\\\3\pi n<2x<\pi+3\pi n,n\in Z\\\\1,5\pi n<x<\frac{\pi }{2}+1,5\pi n,n\in Z\\\\Otvet:\boxed{x\in(1,5\pi n \ ; \ \frac{\pi }{2}+1,5\pi n)}$