Question

已知向量a=(sinx,2倍根号3sinx)向量b=(2cosx,sinx)定义f(x)=向量a乘向量b-根号3

Answer 1

f(x)=a*b=2sinxcosx+2√3(sinx)^2=sin(2x)+√3[1-cos(2x)]=2sin(2x-π/3)+√3 ,

因为 y=f(x+φ)=2sin(2x+2φ-π/3)+√3 为偶函数,

所以 2φ-π/3=π/2 ,

解得 φ=5π/12 .