Question

Решите неравенство:
$tg(\frac{x}{3} + \frac{pi}{4}) \ \textless \ \frac{\sqrt[]{3} }{2}$

Answer 1

$-\frac{\pi }{2}+\pi k <\frac{x}{3} +\frac{\pi }{4} < arctg \frac{\sqrt{3} }{2} +\pi k, k \in Z$

$-\frac{\pi }{4}-\frac{\pi }{2}+\pi k <\frac{x}{3} < arctg \frac{\sqrt{3} }{2}-\frac{\pi }{4} +\pi k, k \in Z$

$-\frac{3 \pi }{4}+\pi k <\frac{x}{3} < arctg \frac{\sqrt{3} }{2}-\frac{\pi }{4} +\pi k, k \in Z$

О т в е т.

$-\frac{9 \pi }{4}+ 3\pi k <x < 3arctg \frac{\sqrt{3} }{2}-\frac{3\pi }{4} +3\pi k, k \in Z$