要使f(x)=sin(x+θ)+cos(x+θ)为偶函数,求θ

要使f(x)=sin(x+θ)+cos(x+θ)为偶函数,求θ

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=360kθ=360k+45,其中k是整数======以下答案可供参考======供参考答案1:令t=x+θf(x)=sint+cost =√2cos(t-π/4)所以f(x)=√2cos(x+t-π/4)只有t-π/4为2π的整数倍的时候f(x)=sin(x+θ)+cos(x+θ)为偶函数所以t=2kπ+π/4 k是整数供参考答案2:f(x)=sin(x+θ)+cos(x+θ)=√2[√2sin(x+θ)/2+√2cos(x+θ)/2]=√2[sin(x+θ)cos(π/4)+cos(x+θ)sin(π/4)]=√2sin(x+θ+π/4)f(0)=±√2√2sin(θ+π/4)=±√2sin(θ+π/4)=±1θ+π/4=2kπ±π/2θ=2kπ+π/4或θ=2kπ-3π/4供参考答案3:根据偶函数性质,f(-x)=f(x)即sin(-x+θ)+cos(-x+θ)=sin(x+θ)+cos(x+θ)解得θ=π/4+2kπ度或π5/4+2kπ度需要知道的是x不等于0或180度,否则题目没意义!

好好学习下

如以上回答内容为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！

点此我要举报以上问答信息