Question

向量的题

已知向量a=(sinx,√3cosx),向量b=(cosx,cosx),f(x)=a*b
求f(x)的最小正周期：求f(x)在区间[π/3，π]的最大值与最小值

Answer 1

f(x)=a·b=sinxcosx+根号3·(cosx)^2
=1/2sin2x+根号3/2(1+cos2x)
=sin2xcosπ/3+sinπ/3cos2x+根号3/2
=sin(2x+π/3)+根号3/2
故f(x)的最小正周期为π
当π/3≤x≤π时，π≤2x+π/3≤7π/3
∴-1≤sin(2x+π/3)≤1/2
从而-1+根号3/2≤sin(2x+π/3)+根号3/2≤1/2+根号3/2