Question

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

Answer 1

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