f(x)=sin^2-sin[2x-(π/6)]的值域过程

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f(x)=sin^2-sin[2x-(π/6)]的值域过程f(x)=sin^2-sin[2x-(π/6)]的值域过程f(x)=sin^2-sin[2x-(π/6)]的值域过程f(x)=(1-cos2x

f(x)=sin^2-sin[2x-(π/6)]的值域过程
f(x)=sin^2-sin[2x-(π/6)]的值域过程

f(x)=sin^2-sin[2x-(π/6)]的值域过程
f(x)=(1-cos2x)/2-(sin2xcosπ/6-cos2xsinπ/6)
=1/2-1/2*cos2x-sin2xcosπ/6+1/2*cos2x
=-(√3/2)sin2x+1/2
-1<=sin2x<=1
-√3/2<=-(√3/2)sin2x<=√3/2
加上1/2
所以值域[(-√3+1)/2,(√3+1)/2]

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