Question

f(x)=向量m乘以向量n,其中向量m=(sinx,cos(x+π/4)).向量n=(cosx.cos(x-π/4)),

Answer 1

1.f(x)=sinxcosx+cos(x+π/4)cos(x-π/4)=(1/2)sin2x+(1/2)cos2x=(1/2)(sin2x+cos2x)

=(√2/2)sin(2x+π/4); 所以T=π； 最大值为√2/2；

f(x)取最大值时,2x+π/4=2kπ+π/2; x=kπ+π/8;

f(x)取最大值时x的取值集合{x|x=kπ+π/8};

2.由2x+π/4=kπ+π/2得f(x)图像的对称轴为：x=kπ/2+π/8；

3.x∈[-π,π]时,-7π/4≤2x+π/4≤9π/4;

由-7π/4≤2x+π/4≤-3π/2; -π/2≤2x+π/4≤π/2; 3π/2≤2x+π/4≤9π/4得：

-π≤x≤-7π/8； -3π/8≤x≤π/8; 5π/8≤x≤π

所以f(x)得增区间为[-π,-7π/8]; [-3π/8,π/8]; [5π/8,π]