函数f(x)=sin(x+θ)+根号3cos(x-θ)的图像关于y轴对称,则θ=

函数f(x)=sin(x+θ)+根号3cos(x-θ)的图像关于y轴对称,则θ=
函数f(x)=sin(x+θ)+根号3cos(x-θ)的图像关于y轴对称,则θ=

函数f(x)=sin(x+θ)+根号3cos(x-θ)的图像关于y轴对称,则θ=
关于y轴对称就是说该函数是偶函数,就是f(x)=f(-x)即sin(x+θ)+根号3cos(x-θ)=sin(-x+θ)+根号3cos(-x-θ),sin(x+θ)+根号3cos(x-θ)=sin(-x+θ)+根号3cos(x+θ)【利用cosx= cos（-x）】两边同时除以2得(1/2)sin(x+θ)+（2分之根号3）cos(x-θ)=(1/2)sin(-x+θ)+（2分之根号3）cos(x+θ),1/2=sin30°,（2分之根号3）=cos30°,所以前式化为sin30°sin(x+θ)+cos30°cos(x-θ)=sin30°sin(-x+θ)+cos30°cos(x+θ),将sin30°sin(x+θ)移到右边sin30°sin(-x+θ)移到左边,得cos30°cos(x-θ)-sin30°sin(-x+θ)=cos30°cos(x+θ)-sin30°sin(x+θ),即cos30°cos(x-θ)+sin30°sin(x-θ)=cos30°cos(x+θ)-sin30°sin(x+θ),cos（x-θ-30°）=cos（30°+x+θ）,得x-θ-30°=（30°+x+θ）+2kπ（k为整数）,30°=π/6,所以θ=π/6+kπ（k为整数）.

f(x)=sin(x-θ)+3cos(x-θ)的图象关于y轴对称
即偶函数，f(x)=f(-x)
sin(x-θ)+3cos(x-θ)
=sin(-x-θ)+3cos(-x-θ)
=-sin(x+θ)+3cos(x+θ)
=2sin[x+θ-(π/3)]
sinx图像对称轴π/2+kπ
y轴对称sin（x-π/2）
[x+θ-(π/3)+(π/3）-π/2]=-π/6
最后加上kπ
答案是 kπ-π/6