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

题目

已知向量m=﹙sin﹙x－π/4﹚,1﹚向量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＞0﹚个单位长度,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.

答案

m//n,则：[sin(x－π/4)]/cos(x－π/4)=1/3,即：tan(x－π/4)=1/3又：tan(x－π/4)=[tanx－1]/[tanx＋1]=1/3,则：tanx=2f(x)=sin(x－π/4)cos(x－π/4)＋3=(1/2)sin(2x－π/2)＋3=－(1/2)cos2x＋3tanx=2f(x)=－(1/2)...