Найдите корни этого уравнения, принадлежащие отрезку [-9π/2; -3π].

For x = -π/3 + 2πn:
-9π/2 ≤ -π/3 + 2πn ≤ -3π
-27/6 ≤ -2/6 + 12πn/6 ≤ -18/6
-25 ≤ 12πn ≤ -16. No integer n satisfies this.
For x = 4π/3 + 2πn:
-9π/2 ≤ 4π/3 + 2πn ≤ -3π
-27/6 ≤ 8/6 + 12πn/6 ≤ -18/6
-35 ≤ 12πn ≤ -26. For n = -2, 12πn = -24π, which is not in the range. For n = -3, 12πn = -36π, which is not in the range. Let's recheck the interval. The interval is [-9π/2, -3π].
For x = -π/3 + 2πn:
If n = -2, x = -π/3 - 4π = -13π/3. -9π/2 = -13.5π/3, -3π = -9π/3. So -13.5π/3 ≤ -13π/3 ≤ -9π/3. This is a solution.
If n = -1, x = -π/3 - 2π = -7π/3. This is not in the interval.
For x = 4π/3 + 2πn:
If n = -3, x = 4π/3 - 6π = -14π/3. -9π/2 = -13.5π/3. So -13.5π/3 ≤ -14π/3 is false.
If n = -2, x = 4π/3 - 4π = -8π/3. This is not in the interval.
The only root in the interval is -13π/3.