函数f(x)=sin(x-θ)+3cos(x-θ)的图象关于y轴对称,则θ=?

f(x)=sin(x-θ)+3cos(x-θ)的图象关于y轴对称
f(x)=f(-x)
sin(x-θ)+3cos(x-θ)
=sin(-x-θ)+3cos(-x-θ)
=-sin(x+θ)+3cos(x+θ)
sin(x+θ)+sin(x-θ)=3[cos(x+θ)-cos(x-θ)]
2sinxcosθ=-6sinxsinθ
sinθ/cosθ=-2/6
tanθ=-1/3
θ=-arctan(1/3)