函数f(x)=Asin(ωx+φ)（A＞0,ω＞0,|φ|＜π/2）的部分图像如图所示. ①求f(

①
函数f(x)=Asin(ωx+φ)（A＞0,ω＞0,|φ|＜π/2）
根据图像知A=1,
半周期T/2=2π/3-π/6=π/2,T=π
根据2π/w=π得：w=2
又x=π/6,f(x)取得最大值1
则sin(2*π/6+φ)=1,φ+π/3=π/2+2kπ,k∈Z
∴φ=π/6+2kπ,k∈Z
∵|φ|＜π/2 ∴φ=π/6
∴f(x)的最小正周期T=π
解析式f(x)=sin(2x+π/6)

②
g(x)=f(x)-cos2x
=sin(2x+π/6)-cos2x
=sin2xcosπ/6+cos2xsinπ/6-cos2x
=sin2xcosπ/6-cos2xsinπ/6
=sin(2x-π/6)
∵0≤x≤π/2
∴-π/6≤2x-π/6≤5π/6
∴当2x-π/6=-π/6时,g(x)取得最小值-1/2