已知a向量=(cos(2x-π/3),sin(x-π/4),b向量=(1,2sin(x+π/4)),函数f(x)=a向量×b向量 (1)求f(x)的对称抽方程(2)求f(x)在区间[-π/12,π/2]上的值域.
问题描述:
已知a向量=(cos(2x-π/3),sin(x-π/4),b向量=(1,2sin(x+π/4)),函数f(x)=a向量×b向量 (1)求f(x)的对称抽方程(2)求f(x)在区间[-π/12,π/2]上的值域.
答
(1)∵f(x)=a·b∴f(x)=cos(2x-π/3)×1+sin(x-π/4)×2sin(x+π/4)=1/2 cos2x+√3/2sin2x+2[﹙√2/2sinx﹚²-﹙√2/2cosx﹚²]=1/2 cos2x+√3/2sin2x-cos2x=√3/2sin2x-1/2cos2x=sin(2x-π/6)∴2x...