Задача 27087 2sin(x/2-pi/4) > -1...

u46211114223

04.05.2018

2sin(x/2-pi/4) > -1

SOVA

04.05.2018

sin((x/2)–(Pi/4)) > -1/2
⇒
(-Pi/6) +2Pin < (x/2)–(Pi/4) < Pi-(-Pi/6) + 2Pin, n ∈ Z
(-Pi/6) +2Pin < (x/2)–(Pi/4) < (7Pi/6) + 2Pin, n ∈ Z
(-Pi/6)+(Pi/4) +2Pin < (x/2) < (7Pi/6)+ (Pi/4) + 2Pin, n ∈ Z
(Pi/12) +2Pin < (x/2) < (17Pi/12)+ 2Pin, n ∈ Z
(Pi/6) +4Pin < x < (17Pi/6)+ 4Pin, n ∈ Z