Sin (3/4x+pi/9) > = корень из 3/2

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 ].