已知向量a=cos,sin若a＝,求函数的最小值

题目

已知向量a=cos,sin若a＝,求函数的最小值

答案

这题不错,够16分：
1
α=π/4,即：c=(sinx+√2,cosx+√2)
f(x)=b·c=(cosx,sinx)·(sinx+√2,cosx+√2)
=sin(2x)+√2(sinx+cosx)
=sin(2x)+2sin(x+π/4)
=-cos(2x+π/2)+2sin(x+π/4)
=-(1-2sin(x+π/4)^2)+2sin(x+π/4)
=2sin(x+π/4)^2+2sin(x+π/4)^2-1
=2(sin(x+π/4)+1/2)^2-3/2
0