已知函数f(x)=2sin平方(派/6x)+sin((派/3x+派/6)-1,求f(x)值域
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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](/uploads/image/z/8858032-16-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%E5%B9%B3%E6%96%B9%28%E6%B4%BE%2F6x%29%2Bsin%28%28%E6%B4%BE%2F3x%2B%E6%B4%BE%2F6%29-1%2C%E6%B1%82f%28x%29%E5%80%BC%E5%9F%9F)
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]
=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]
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