∵f(x)=sin(wx+Ф)(w>0,0≤Ф≤π)为偶函数
∴f(-x)=-f(x)
∴sin(-wx+Φ)=sin(wx+Φ)
∴-sinwxcosΦ+coswxsinφ=sinwxcosΦ+coswxsinφ
∴sinwxcosΦ=0
∴sinwx是变量
∴cosΦ=0
∵0≤Ф≤π∴Φ=π/2
∵图像上相邻的两个最高点之间的距离为2π
∴函数最小正周期T=2π ∴w=1
∴f(x)=sin(x+π/2)=cosx
(2)
∵f(α+π/3)=1/3
∴cos(α+π/3)=1/3
∵α∈(-π/3,π/2),
∴α+π/3∈(0,5π/6)
∴sin(α+π/3)=√[1-cos²(α+π/3)]=2√2/3
∴sin(2α+2π/3)
=2sin(α+π/3)cos(α+π/3)
=2*2√2/3*1/3
=4√2/9
∴sin(2α+5π/3)
=sin[π+(2α+2π/3)]
=-sin(2α+2π/3)
=-4√2/9