Question

已知函数数f(x)=Asin(wx+π/6)(A＞,w＞0,x∈R)的最小正周期为T=6π,

且f(2π)=2.
1.若α,β[0,π/2],f(3α+π)=16/5,f(3β+5π/2)=-20/13,求sin(α-β)的值
若α,β∈[0,π/2],

Answer 1

w=2π/(6π)=1/档如喊行野3
f(2π)=Asin(1/橡掘3*2π+π/6)=2
A=4
f(x)=4sin(1/3x+π/6)

追问

若α,β∈[0,π/2],

追答

f(3α+π)=4sin[1/3*(3α+π)+π/6]=16/5
sin(α+π/2)=4/5
cosα=4/5,sinα=3/5
f(3β+5π/2)=4sin[1/3*(3β+5π/2)+π/6]=-20/13
sin(β+π)=-5/13
sinβ=5/13,cosβ=12/13
sin(α-β)=3/5*12/13-4/5*5/13=16/65