函数fx=sin(2x-π/3),(1).求函数fx的最小正周期,(2),求函数fx的值域,并求出最大值最小值及相应的x值

Question

函数fx=sin(2x-π/3),(1).求函数fx的最小正周期,(2),求函数fx的值域,并求出最大值最小值及相应的x值

Answer 1

(1)
f(x)=sin^2x+√3sinxcosx+1/2
=-1/2(1-2sin^2x)+√3/2sin2x+1
=cos(π/6)sin2x- sin(π/6)cos2x+1
= sin(2x-π/6)+1
f(x)的最小正周期=2π/2=π
(2)
f(x)= sin(2x-π/6)+1
2x-π/6=π/2+2kπ
x=π/3+kπ
f(x)=2为最大值
2x-π/6=-π/2+2kπ
x=-π/6+kπ
f(x)=0为最小值
(3)
-π/6+kπ