函数f(x)=2sin(2x-π/4),若f(x+φ)为奇函数,
y=sinx为奇函数
f(x+φ)=2sin(2(x+φ)-π/4)=2sin(2x+2φ-π/4)
2φ-π/4=kπ
2φ-π/4=0 φ=π/8
或2φ-π/4=π φπ/8
2φ-π/4=2π φ=9π/8/4=3π φ=13π/8
若为偶函数,
y=cosx为偶函数
2φ-π/4=kπ+π/2
φ=kπ/2+3π/4
k=-1 φ=π/4
k=0 φ=5π/4
k=2 φ=11π/8