Question

已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤π)为偶函数,其图象上相邻的两个最高点之间为2π.

Answer 1

周期为2π,所以w=1,

f(x)为偶函数,所以ψ=2kπ+π/2;

所以 (1) f(x)=sin(x+π/2)=cosx;

(2)α∈(-π/3,π/2),α+π/3∈(0,5π/6)

因为：cos(α+π/3)=1/3; 所以sin(α+π/3)=2√2/3;

sin(2α+5π/3)=sin[(2x+2π/3)+π]= - sin(2x+2π/3)= -sin[2(x+π/3)]

= - 2sin(α+π/3)cos(α+π/3)= -2×(2√2/3)×(1/3)= - 4√2/9