Question

设函数f(x)=Asin(wx+φ)(A>0,w>0).φ分别取何值时,f（x）为奇函数和偶函数?

Answer 1

f(x)为奇函数时：-f(x)=-Asin(wx+φ)=f(-x)=Asin(-wx+φ)

sin(wx+φ)=-sin(-(wx-φ))=sin(wx-φ)

wx+φ=wx-φ+T

所以φ=k*T/2=kπ/ω,k为任意整数

f(x)为偶函数时：f(x)=Asin(wx+φ)=f(-x)=Asin(-wx+φ)

Asin(wx+φ)=Asin(-(wx-φ)) sin(wx+φ)=sin(-wx+φ)=-sin(wx-φ)

wx+φ=-wx+φ+T

无解