Function domain y = arccos (2sinx)

In order to find the domain of the function y = arccos (2 * sinx), we use the fact that the function y = arccosx is defined at –1 ≤ х ≤ 1.
So, the given function y = arccos (2 * sinx) is defined if the following double inequality is satisfied –1 ≤ 2 * sinx ≤ 1. Divide all 3 parts of this double inequality by 2> 0. Then we get the following double inequality: –1/2 ≤ sinx ≤ 1/2.
The solutions of the resulting double inequality in the figure  are highlighted in red. This means that the domain of the function y = arccos (2 * sinx) is: π * n – π / 6 ≤ x ≤ π * n + π / 6, where n is an integer.
Answer: х ∈ [π * n – π / 6; π * n + π / 6], where n is an integer.