设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|

题目

设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|

答案

f(x)=sin(wx+φ)+cos(wx+φ)
=√2sin(wx+φ+π/4)
T=2π/w=π
w=2
f(x)=√2sin(2x+φ+π/4)
f(-x)=f(x),
所以 f(-π/8)=f(π/8)
sinφ=sin(π/2+φ)=cosφ
tanφ=1
|φ|