Question

Sin ( x- п/3) >= (больше или равен) корень из 3/2

Answer 1

Аалвьралаоьвдалабадопл

Answer 2

To solve the inequality sin(x - π/3) ≥ √3/2, we can start by finding the reference angle for the given inequality. The reference angle is the positive acute angle between the terminal side of an angle and the x-axis.

The reference angle for sin(x - π/3) is π/6. This means that the solutions for the inequality lie in the intervals [π/3 + 2πk, 5π/3 + 2πk], where k is an integer.

To determine whether sin(x - π/3) is greater than or equal to √3/2 in these intervals, we can examine the values of sin(x) in the corresponding intervals [π/3, 5π/3].

In the interval [π/3, 5π/3], sin(x) is greater than or equal to √3/2 when x belongs to the intervals [π/3 + 2πk, π/2 + 2πk] and [3π/2 + 2πk, 5π/3 + 2πk], where k is an integer.

In summary, the solutions to the inequality sin(x - π/3) ≥ √3/2 are given by the intervals [π/3 + 2πk, π/2 + 2πk] and [3π/2 + 2πk, 5π/3 + 2πk], where k is an integer.