The minimum positive period of the function f (x) = 2Sin ^ 2 (Wx) + 2 radical 3sinwxsin (π / 2-wx) (w ＞ 0) is known to be PI ① Finding monotone increasing interval and symmetric central coordinate of function f (x) ② Find the value range of function f (x) in the interval [0,2 π / 3]

The minimum positive period of the function f (x) = 2Sin ^ 2 (Wx) + 2 radical 3sinwxsin (π / 2-wx) (w ＞ 0) is known to be PI ① Finding monotone increasing interval and symmetric central coordinate of function f (x) ② Find the value range of function f (x) in the interval [0,2 π / 3]

F (x) = 2Sin ^ 2 (Wx) + 2 radical 3sinwxsin (π / 2-wx) = 1-cos (2wx) + 2 √ 3sinwx * cos (Wx) = √ 3sin (2wx) - cos (2wx) + 1 = 2Sin (2wx - π / 6) + 1, and the period is t = 2 π / (2W) = π (w = 1  f (x) = 2Sin (2x - π / 6) + 1 (1) 2K π - π / 2 ≤ 2x - π / 6 ≤ 2K π + π / 2