A symmetry axis of the graph with function y = 1 / 2Sin (x - π / 3) is a straight line Why is the answer x = - π / 6

A symmetry axis of the graph with function y = 1 / 2Sin (x - π / 3) is a straight line Why is the answer x = - π / 6

A symmetry axis of the graph with function y = 1 / 2Sin (x - π / 3) is a straight line
X-π/3=2kπ+π/2==>x=2kπ+5π/6=2kπ+π-π/6
X-π/3=2kπ-π/2==>x=2kπ-π/6
So the axis of symmetry is k π - π / 6
When k = 0, an axis of symmetry is a straight line - π / 6

The axis of symmetry of the function y = 2Sin (2x Pie / 3) is
I don't understand. Let's just use derivative. I don't like derivative

Y = 2Sin (2x - π / 3) y = 2Sin (2x - π / 3) y '= 4cos (2x - π / 3) let y' = 0, that is, 4cos (2x - π / 3) = 0, where cos (2x - π / 3) = 0, the solution is: x = k π / 2 + 5 π / 12, k = 0, ± 1, ± 2, ± 3 The general formula of the axis of symmetry is: x = k π / 2 + 5 π