Question

sin(3/4x+pi/9)>= корень из 3/2

Answer 1

sin((3/4)*x +π/9) ≥(√3)/2 ;
arcsin(√3)/2 ≤ (3/4)*x +π/9 ≤ π - arcsin√(3)/2 ;
π/3 ≤ (3/4)*x + π/9 ≤ π - π/3  ;
π/3 -π/9 ≤ (3/4)*x  ≤ π  - π/3 -π/9 ;
2π/9  ≤   (3/4)*x   ≤ 5π/9 ;
4*(2π/9)/3  ≤ x  ≤ 4*(5π/9)/3 ;
8π/27  ≤ x  ≤ 20π/27 ;

ответ:   x ∈ [ 8π/27  ; 20π/27 ] .