2) а) Sin(3x -2π/3) ≥1/2
π/6 + 2πn ≤ 3x -2π/3 ≤5π/6 + 2πn , n ∈Z
π/6 + 2πn +2π/3 ≤ 3x ≤5π/6 + 2πn+2π/3 , n ∈Z
π/18 + 2πn/3 +2π/9 ≤ x ≤5π/18 + 2πn/3+2π/9 , n ∈Z
б)Cos(2x +3π/4) ≤ -√2/2
3π/4 + 2πk ≤2x +3π/4 ≤5π/4 + 2πk , k ∈Z
3π/4 + 2πk ≤2x +3π/4 ≤5π/4 + 2πk , k ∈Z
3π/4 + 2πk ≤2x +3π/4 ≤5π/4 + 2πk , k ∈Z
3π/4 + 2πk ≤2x +3π/4 ≤5π/4 + 2πk , k ∈Z
3π/4 + 2πk - 3π/4 ≤ 2x ≤5π/4 + 2πk - 3π/4, k ∈Z
2πk ≤ 2x ≤ 2π/4 + 2πk, k ∈Z
πk ≤ x ≤ π/4 + πk, k ∈Z
3)4(1 - Sin²x) -(2√2 -2)Sinx > 4 - √2
4 - 4Sin²x -(2√2 -2)Sinx > 4 - √2
4Sin²x + (2√2 -2)Sinx - √2 < 0
Sinx = (-√2+1 +-√(2 -2√2 +1 +4√2) )/4 = (-√2 +1 +-√(√2+1)²)/4 = -√2 +1 +-(√2 +1) )/4
a) Sinx = 1/2 б) Sinx = -√2/2
-√2/2 < Sinx < 1/2
-π/4 + 2πk < x < π/6 + 2πk , k ∈ Z