Question

已知向量a=(sin x,2√3sin x),b=(2cos x,sin x),定义f

Answer 1

f(x)=sinx(2cosx)+2√3sin²x-√3

=sin2x-√3(1-2sin²x）

=sin2x-√3cos2x

=2sin(2x-π/6)

(1)

把2x-π/6代入到标准正弦函数的单调减区间中去解出x

π/2+2kπ≤2x-π/6≤3π/2+2kπ

π/3+kπ≤x≤5π/6+kπ

单调减区间是：[π/3+kπ ,5π/6+kπ]

(2)

f(x+θ)=2sin(2x+2θ-π/6)

当x=0时,|f(x+θ)|=2

sin(2θ-π/6)=±1

θ=π/3