已知函数f(x)=2sinxcosx-2根号3cos^2x+根号3(1)求f(x单调区间)
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已知函数f(x)=2sinxcosx-2根号3cos^2x+根号3(1)求f(x单调区间)
已知函数f(x)=2sinxcosx-2根号3cos^2x+根号3(1)求f(x单调区间)
已知函数f(x)=2sinxcosx-2根号3cos^2x+根号3(1)求f(x单调区间)
f(x)=2sinxcosx-2根号3cos^2x+根号3
=sin2x-√3(1+cos2x)+√3
=sin2x-√3cos2x
=2[(1/2)sin2x-(√3/2)cos2x]
=2sin(2x-π/3)
所以递增区间为2x-π/3∈[2kπ-π/2,2kπ+π/2]
即x∈[kπ-π/12,kπ+5π/12]
递减区间为2x-π/3∈[2kπ+π/2,2kπ+3π/2]
即x∈[kπ+5π/12,kπ+11π/6]
f(x)=2sinxcosx-2√3cos^2x+√3
=sin2x-√3cos2x
=2sin(2x-π/3)
因此周期是2π/2=π
2kπ-π/2≤2x-π/3≤2kπ+π/2时单增,
即2kπ-π/6≤2x≤2kπ+5π/6
kπ-π/12≤x≤kπ+5π/12时单增
kπ+5π/12≤x≤kπ+11π/12时单减
-2根号3cos^2x+根号3=-根号3(2cos^2x-1)=-根号3cos2x
f(x)可以化为f(x)=sin2x-根号3cox2x=2(0.5sin2x-0.5根号3cos2x)=2sin(2x-60°)
根据正弦函数单调性 在区间[-15°,75°]上,函数是单调递增的,在区间[75°,165°]上是单调递减的
已知函数f(x)=2sinxcosx-2(√3)cos²x+√3;求f(x)的单调区间)
f(x)=sin2x-(√3)(1+cos2x)+√3=sin2x-(√3)cos2x=2[(1/2)sin2x-(√3/2)cos2x]
=2[sin2xcos(π/3)-cos2xsin(π/3)]=2sin(2x-π/3)
①由-π/2+2kπ≦2x-π/3≦π/2+2...
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已知函数f(x)=2sinxcosx-2(√3)cos²x+√3;求f(x)的单调区间)
f(x)=sin2x-(√3)(1+cos2x)+√3=sin2x-(√3)cos2x=2[(1/2)sin2x-(√3/2)cos2x]
=2[sin2xcos(π/3)-cos2xsin(π/3)]=2sin(2x-π/3)
①由-π/2+2kπ≦2x-π/3≦π/2+2kπ,得单增区间为[-π/12+kπ,5π/12+kπ] (k∈Z)
②由π/2+2kπ≦2x-π/3≦3π/2+2kπ,得单减区间为[π/12+kπ,11π/12+kπ] (k∈Z)
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