要使f(x)=sin(x+θ)+根号3cos(x+θ)为偶函数,求θ

要使f(x)=sin(x+θ)+根号3cos(x+θ)为偶函数,求θ
要使f(x)=sin(x+θ)+根号3cos(x+θ)为偶函数,求θ

要使f(x)=sin(x+θ)+根号3cos(x+θ)为偶函数,求θ
f(x)=sin(x+θ)+根号3cos(x+θ)
=2[sinπ/6sin(x+θ)+cosπ/6*cos(x+θ)]
=2cos(x+θ-π/6)
为偶函数
θ-π/6=kπ,k∈Z
θ=π/6+kπ,k∈Z