1
f(x)=m·n=(2sin(wx+π/3),1)·(2cos(wx),-√3)
=4sin(wx+π/3)cos(wx)-√3
=4(sin(wx)/2+√3cos(wx)/2)cos(wx)-√3
=sin(2wx)+√3(1+cos(2wx))-√3
=sin(2wx)+√3cos(2wx)
=2sin(2wx+π/3)
相邻对称轴距离为π/2,即：最小正周期：T=π
即：2π/(2w)=π,即：w=1
即：f(x)=2sin(2x+π/3)
增区间：2x+π/3∈[2kπ-π/2,2kπ+π/2]
即：x∈[kπ-5π/12,kπ+π/12],k∈Z
2
x∈[-5π/6,π/12],2x+π/3∈[-4π/3,π/2]
sin(2x+π/3)∈[-1,1],即：2sin(2x+π/3)∈[-2,2]
即：f(x)∈[-2,2]