Розв'яжіть нерівність 2cos^2*6x≤1,5
Только пожалуйста распешите!
oganesbagoyan:
2cos²6x ≤ 1,5 ?
Ответы
Ответ дал:
0
2cos²6x ≤1,5;
cos²6x ≤3/4;
|cos6x| ≤1/2*√3
- 1/2*√3≤ cos6x ≤1/2*√3 .
a) π/6 ≤ 6x ≤ π -π/6 ;
π/6 ≤6x ≤5π/6 ;
2π*k +π/6 ≤6x ≤5π/6+ 2π*k ;
π/3*k +π/36 ≤ x≤ 5π/36 +π/3*k , k∈Z
b) π+π/6 ≤ 6x ≤ 2π -π/6 ;'
7π/6 ≤ 6x ≤ 11π/6 ;
2π*k + 7π/6 ≤ 6x ≤ 11π/6 + 2π*k ;
π/3*k + 7π/36 ≤ x ≤ 11π/36 + π/3*k ;
=================================x========
x ∈[ π/3*k +π/36 ; 5π/36 +π/3*k ] U [π/3*k + 7π/36 ;11π/36 + π/3*k ] k∈Z
cos²6x ≤3/4;
|cos6x| ≤1/2*√3
- 1/2*√3≤ cos6x ≤1/2*√3 .
a) π/6 ≤ 6x ≤ π -π/6 ;
π/6 ≤6x ≤5π/6 ;
2π*k +π/6 ≤6x ≤5π/6+ 2π*k ;
π/3*k +π/36 ≤ x≤ 5π/36 +π/3*k , k∈Z
b) π+π/6 ≤ 6x ≤ 2π -π/6 ;'
7π/6 ≤ 6x ≤ 11π/6 ;
2π*k + 7π/6 ≤ 6x ≤ 11π/6 + 2π*k ;
π/3*k + 7π/36 ≤ x ≤ 11π/36 + π/3*k ;
=================================x========
x ∈[ π/3*k +π/36 ; 5π/36 +π/3*k ] U [π/3*k + 7π/36 ;11π/36 + π/3*k ] k∈Z
Вас заинтересует
11 месяцев назад
1 год назад
1 год назад
6 лет назад
6 лет назад
7 лет назад