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],

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)=1/3
f(2π)=Asin(1/3*2π+π/6)=2
A=4
f(x)=4sin(1/3x+π/6)