It is known that the coordinates of the highest point and the lowest point of the image of the function f (x) = asin (ω X - π / 3) (a > 0, ω > 0) in a certain period are (5 π / 12,2), respectively, (11π/,-2) (1) Find the values of a and ω; (2) Given α ∈ (0, π / 2) and sin α = 4 / 5, find the value of F (α)

It is known that the coordinates of the highest point and the lowest point of the image of the function f (x) = asin (ω X - π / 3) (a > 0, ω > 0) in a certain period are (5 π / 12,2), respectively, (11π/,-2) (1) Find the values of a and ω; (2) Given α ∈ (0, π / 2) and sin α = 4 / 5, find the value of F (α)

The coordinate of the lowest point is (11 π 12 /, - 2) 1) the abscissa difference between the highest point and the lowest point in the same period is half period ﹣ T / 2 = 11 π / 12 - 5 π / 12 = π / 2 ﹣ t = π, which is obtained from 2 π / w = π, w = 2, and the highest point is (5 π / 12,2) ﹣ a = 2,2) ∵ α ∈ (0, π / 2), sin α = 4 / 5 ﹣ cos α = 3 / 5 ﹣ sin2 α = 2