Question

已知函数f(x)=Asin(wx+n)(A>0,w>0)在x=1的时候取最大值A,则f（x+1）的奇偶性是

Answer 1

由函数f(x)=Asin(wx+n)(A>0,w>0)在x=1的时候取最大值A

可知sin(w+n)=1

由(sin(w+n))^2+(cos(w+n))^2=1

cos(w+n)=0

f(x+1)=Asin(w(x+1)+n)=Asin(wx+n+w)

=A[sin(wx)cos(wx+n)+cos(wx)sin(wx+n)]

=A[cos(wx)*1]

=Acos(wx)

显然f(x+1)=Acos(wx)是偶函数