It is known that the period of the function f (x) = asin (ω x + φ), X ∈ R (where a ＞ 0, ω ＞ 0, 0 ＜φ＜π / 2) is π and the lowest point on the image is m (2 Π / 3, - 2). The analytic expression of F (x) is obtained. When x ∈ [0, Π / 12], the maximum value of F (x) is?

It is known that the period of the function f (x) = asin (ω x + φ), X ∈ R (where a ＞ 0, ω ＞ 0, 0 ＜φ＜π / 2) is π and the lowest point on the image is m (2 Π / 3, - 2). The analytic expression of F (x) is obtained. When x ∈ [0, Π / 12], the maximum value of F (x) is?

Because the period is π, then t = 2 π / ω = π ω = 2, so f (x) = asin (2x + φ) because the lowest point is m (2 π / 3, - 2), then the lowest point is sin (2 * 2 π / 3 + φ) = sin (4 π / 3 + φ) = - 1, then 4 π / 3 + φ = 2K π - π / 2 φ = 2K π - π / 2-4 π / 3 = 2K π - 11 π / 6 = 2K π - 2 π + π / 6 = 2 (k-1) π + π / 6