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.

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