已知向量a=(sin1/2x,根号3/2) b=(1/2 ,cos1/2x) f(x)=a*b,

f(x)=a·b=(1/2)sinx/2+(√3/2）cosx/2
=sinx/2cosπ/3+cosx/2sinπ/3
=sin(x/2+π/3),
最小正周期T=2π/(1/2)=4π,
2kπ-π/2<=x/2+π/3<=2kπ+π/2,为单调增函数,（k∈Z）,
4kπ-5π/3≤x≤4kπ+π/3,（k∈Z）,为单调增函数,
取k=0,
若x∈（-2π,2π）,则-5π/3≤x≤π/3,为单调增函数.