Question

Решите неравенство Sin(2x+п/4)≤√3/2

Answer 1

pi/3+2pik ≤ 2x+pi/4 ≤ 2pi/3+2pik- вычту pi/4

pi/12+2pik ≤ 2x ≤ 5pi/12+2pik-делю все на 2

pi/24+pik ≤ x ≤ 5pi/24+pik

x∈ [pi/24+pik;5pi/24+pik]; k∈Z

Answer 2

Ответ:

$sin(2x+\dfrac{\pi}{4})\leq \dfrac{\sqrt3}{2}\\\\\dfrac{\pi}{3}+2\pi n\leq 2x+\dfrac{\pi}{4}\leq \dfrac{2\pi }{3}+2\pi n\\\\\dfrac{\pi}{12}+2\pi n\leq 2x\leq \dfrac{5\pi }{12}+2\pi n\\\\\dfrac{\pi }{24}+\pi n\leq x\leq \dfrac{5\pi }{24}+\pi n\ \ ,\ n\in Z\\\\x\in \Big[\ \dfrac{\pi }{24}+\pi n\ ;\ \dfrac{5\pi }{24}+\pi n\ \Big]\ ,\ n\in Z$