作业帮已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求方程f（x）=x/50π的个数加图加说明,答案是399个,如何拆的等式也要说明
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已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求方程f（x）=x/50π的个数加图加说明,答案是399个,如何拆的等式也要说明
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求方程f（x）=x/50π的个数
加图加说明,答案是399个,如何拆的等式也要说明
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求方程f（x）=x/50π的个数加图加说明,答案是399个,如何拆的等式也要说明
f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx
=cosx(sinx+√3cosx)-√3(sinx)^2+sinxcosx
=2sinxcosx+√3[(cosx)^2-(sinx)^2]
=sin2x+√3cos2x
=2sin(2x+π/3)=x/50π,
sin(2x+π/3)=x/100π,
由于|sin(2x+π/3)|
f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx
=2cosx(1/2*sinx+√3/2*cosx) -√3sin^2x+sinxcosx
= sinxcosx+√3cos^2x-√3sin^2x+sinxcosx
=2 sinxcosx+√3(cos^2x-sin^2x)
=sin2x+√3 cos2x
=2 sin(2x+π...
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f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx
=2cosx(1/2*sinx+√3/2*cosx) -√3sin^2x+sinxcosx
= sinxcosx+√3cos^2x-√3sin^2x+sinxcosx
=2 sinxcosx+√3(cos^2x-sin^2x)
=sin2x+√3 cos2x
=2 sin(2x+π/3)
令2x+π/3=kπ+π/2, k∈Z.
得：x=kπ/2+π/12, k∈Z.这就是对称轴方程。
令2x+π/3=kπ, k∈Z.
得：x=kπ/2-π/6, k∈Z.
对称中心为(kπ/2-π/6,0), k∈Z.
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