已知向量m=(sin(x-π/4),1),n=(cos(x-π/4),3),f(x)=mn

问题描述:

已知向量m=(sin(x-π/4),1),n=(cos(x-π/4),3),f(x)=mn
(1)若m//n,求f(x)
(2)若函数的图像向右平移m(m大于0)个单位,再向下平移3个单位后图像对应的函数g(x)是奇函数,求m的最小值.

(1)sin(x-π/4)/cos(x-π/4)=1/33sinx-3cosx=cosx+sinxsinx=2cosxsinx=2√5/5cosx=√5/5f(x)=18/5(2)f(x)=-0.5cos2x+3g(x)=-0.5cos2(x-m)是奇函数cos(2x-2m)=sin(2x+2kπ)-2m+π/2=2kπm=π/4-kπ因为m>0所以m的最小...