Задача 63145 ...

61fe23afbeb6a438048bd533

11.02.2022 18:13:01

2sin(x/2–п/4)≥ 1

61f60a8ebbaef80db6ac39e8

11.02.2022 18:18:41

–π/6) +2πn < (x/2)–(π/4) < π–(–π/6) + 2πn, n ∈ Z
(–π/6) +2πn < (x/2)–(π/4) < (7π/6) + 2πn, n ∈ Z
(–π/6)+(π/4) +2πn < (x/2) < (7π/6)+ (π/4) + 2πn, n ∈ Z
(π/12) +2πn < (x/2) < (17π/12)+ 2πn, n ∈ Z
(π/6) +4πn < x < (17π/6)+ 4πn, n ∈ Z

5f3ea7e3faf909182968ddd9

11.02.2022 18:23:26

[m]sin(\frac{x}{2}-\frac{π}{4}) ≥ \frac{1}{2}[/m]

[m] \frac{π}{6}+2πk ≤ (\frac{x}{2}-\frac{π}{4}) ≤ \frac{5π}{6}+2πk, k ∈ [/m] [b]Z[/b] ⇒

Прибавляем ко всем частям неравенства [m]\frac{π}{4}[/m]

[m] \frac{π}{6}+\frac{π}{4} +2πk ≤ \frac{x}{2} ≤ \frac{5π}{6}+\frac{π}{4} +2πk, k ∈ [/m] [b]Z[/b] ⇒

[m] \frac{5π}{12} +2πk ≤ \frac{x}{2} ≤ \frac{13π}{12}+2πk, k ∈ [/m] [b]Z[/b] ⇒

Умножаем на 2:

[m] \frac{5π}{6} +4πk ≤x ≤ \frac{13π}{6}+4πk, k ∈ [/m] [b]Z[/b] Это ответ