向量a=(根号3sinx,sinx),向量b=(sinx,cosx),设fx=向量a*向量b,

fx=向量a*向量b=√3sin²x+sinxcosx
(1) √3sin²x+sinxcosx=0
√3sinx+cosx=0
tanx=-√3/3
零点为5π/6
(2) f(x)=(√3/2)(1-cos2x)+(1/2)sin(2x)
=sin(2x)cos(π/3)-cos(2x)*sin(π/3)+√3/2
=sin(2x-π/3)+√3/2
最大值 1+√3/2
最小值 1-√3/2