已知函数fX=二分之根号三sin2x－cos2x-1/2,x∈R

题目

已知函数fX=二分之根号三sin2x－cos2x-1/2,x∈R
求fx的最小值和最小正周期

答案

f(x)
=2sinx/2cosx/2 √3cosx
=sin(x/2 x/2) √3cosx
=sinx √3cosx
=√(1^2 √3^2)sin(x π/3)
=2sin(x π/3)
函数f(x)的最小正周期 T=2π/1=2π
f(x)的值域 [-2,2]