Question

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

Answer 1

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)