已知函数f(x)=-根号3sin^2x+sinxcosx.（1）求函数f(x)的最小正周期（2）求函

Question

已知函数f(x)=-根号3sin^2x+sinxcosx.（1）求函数f(x)的最小正周期（2）求函

Answer 1

f(x)=-√3sin?x+sinxcosx
=sin2x*1/2+cos2x*√3/2-√3/2
=sin(2x+π/3)-√3/2
所以T=2π/2=π
(2)因为x∈(0,π/2) ==>2x+π/3∈(π/3,4π/3)
则sin(2x+π/3)∈(-√3/2,1]
==>sin(2x+π/3)-√3/2∈(-√3,(2-√3)/2]