设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 12:11:26

设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|
设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|

设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|
析：f(x)=sin(wx+φ)+cos(wx+φ)=√2sin(wx+φ+π/4)
f(-x)=f(x)：知f(x)图像关于y轴对称,又w>0,所以,f(x)一定可以化简成f(x)=cos(wx)
这样就必须满足φ+π/4=kπ+π/2.φ=kπ+π/4,又知|φ|＜π/2,所以只有φ= π/4

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