已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域

已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域
已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域

已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域
f(x)=2sin2(π/6x)+sin(π/3x+π/6)-1
=sin(π/3x+π/6)-[1-2sin2(π/6x)]
=sin(π/3x+π/6)-cos(π/3x)
=sin(π/3x)*cosπ/6+cos(π/3x)sinπ/6-cos(π/3x)
=sin(π/3x)*√3/2+1/2cos(π/3x)-cos(π/3x)
=sin(π/3x)*√3/2-1/2cos(π/3x)
=sin(π/3x-π/6)
-1≤ sin(π/3x-π/6)≤ 1
f(x)值域为:[-1,1]