как решить sin (3x -2 pi/3) > или равен 1/2

Question

как решить sin (3x -2 pi/3) > или равен 1/2

Answer 1

заменим пока (3x -2 pi/3) на A

SinA ≥ 1/2

A ≥ π/6 +2πn      3x -2 pi/3 ≥ π/6 +2πn, x ≥ 5π/18 +2πn/3 

A ≤ 5π/6 + 2πn   3x -2 pi/3 ≤ 5π/6 + 2πn, x ≤ 9π/18 +2πn/3

5π/18 +2πn/3 ≤ x ≤ 9π/18 +2πn/3

5π/18 +2πn/3 ≤ x ≤ π/2 +2πn/3

Answer 2

SinA ≥ 1/2

A ≥ π/6 +2πn      3x -2 pi/3 ≥ π/6 +2πn, x ≥ 5π/18 +2πn/3 

A ≤ 5π/6 + 2πn   3x -2 pi/3 ≤ 5π/6 + 2πn, x ≤ 9π/18 +2πn/3

5π/18 +2πn/3 ≤ x ≤ 9π/18 +2πn/3

5π/18 +2πn/3 ≤ x ≤ π/2 +2πn/3