Trigonometric function: y=-2 sin (x-pi/3) between x=0 and x=2pi

For what value(s) of x does y have its maximum value?
For what value(s) of x does y have its minimum value?
For what value(s) of x does y = 1?

y = sinx has maximum value when x = π/2 during the interval 0 < x < 2π

y = sinx has minimum value when x = 3π/2 during this interval.

y = sin(x - π/3) is a horizontal translation of π/3 units to the right

=> The maximum value of y is when x = π/2 + π/3 = 5π/6

=> The minimum value of y is when x = 3π/2 + π/3 = 11π/6

Now, y = -2sin(x - π/3) is a vertical stretch of 2 vertically AND a reflection in the x - axis.

So, the maximum and minimum points swap over.

=> y has it's maximum at x = 11π/6 and minimum at x = 5π/6

1 = -2sin(x - π/3)

=> sin(x - π/3) = -1/2

=> x - π/3 = -π/6 + 2nπ or 7π/6 + 2nπ....for n = 0, 1, 2,...

=> x = π/6 + 2nπ or 5π/6 + 2nπ

so, y = 1 at x = π/6 and x = 5π/6

:)>