原题应该是这样子的吧：把函数y=sin(x+4π/3)的图像向左平移ψ个单位所得的图像关于y轴对称,则ψ的最小正值为?
【解】函数y=sin(x+4π/3)的图像向左平移ψ个单位可得：y=sin(x+ψ+4π/3),
它的图像关于y轴对称,说明y=f(x)=sin(x+ψ+4π/3)是偶函数,
即有f(-x)=f(x),
sin(-x+ψ+4π/3) =sin(x+ψ+4π/3),
sin(ψ+4π/3)cosx-cos(ψ+4π/3)sinx= sin(ψ+4π/3)cosx+cos(ψ+4π/3)sinx,
∴cos(ψ+4π/3)sinx=0,
cos(ψ+4π/3) =0,
ψ+4π/3=kπ+π/2.k∈Z.
ψ=kπ-5π/6,k∈Z.
k=1时,ψ的最小正值为π/6.