Question

要使f(x)=sin(x+θ)+cos(x+θ)为偶函数,求θ

Answer 1

f(x)

=sin(x+θ)+cos(x+θ)

=(根号2)[(根号2/2)sin(x+θ)+(根号2/2)cos(x+θ)]

=(根号2)(cos(45)sin(x+θ)+sin(45)cos(x+θ))

=(根号2)sin(x+θ+45)

=(根号2)cos(45-x-θ)

=(根号2)cos(x+θ-45)

f(x)是偶函数,所以θ-45=360k

θ=360k+45,其中k是整数