f(x)=sinwx+√3coswx
=2[sinwx*(1/2)+coswx*(√3/2)]
=2[sinwxcos(π/3)+coswx*sin(π/3)]
=2sin(wx+π/3)
(1)T=2π/w=π
所以 w=2
(2) f(x)=2sin(2x+π/3)
增区间 2kπ-π/2≤2x+π/3≤2kπ+π/2
2kπ-5π/6≤2x≤2kπ+π/6
kπ-5π/12≤x≤kπ+π/12
增区间【kπ-5π/12,kπ+π/12】,k∈Z
(3) x∈【0,π/6】
2x+π/3∈【π/3,2π/3】
sin(2x+π/3)∈【√3/2,1】
f(x)的值域【√3,2】