作业帮求函数f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3的单调递减区间
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 05:32:57
求函数f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3的单调递减区间
求函数f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3的单调递减区间
求函数f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3的单调递减区间
f(x)=2sinxcosx+2√3sin²x-√3
=2sinxcosx+√3sin²x+√3(sin²x-1)
=2sinxcosx+√3sin²x-√3cos²x
=2sinxcosx+√3(sin²x-cos²x)
=sin2x-√3cos2x
=2(1/2 sin2x-√3/2 cos2x)
=2sin(2x-π/3)
sinx的单调递减区间为[π/2+2nπ,3π/2+2nπ] ,n为整数
π/2+2nπ≤2x-π/3≤3π/2+2nπ
5π/6+2nπ≤2x≤11π/6+2nπ
5π/12+nπ≤x≤11π/12+nπ
所以sin(2x-π/3)的单调递减区间为[5π/12+nπ,11π/12+nπ],即
函数f(x)=2sin(2x-π/3)的单调递减区间为[5π/12+nπ,11π/12+nπ],n∈Z
骚年，，，，5分没人愿意费这脑筋的，，，，
f(x)=2sinxcosx+√3(2sin²x-1)
=sin2x-√3cos2x
=2(1/2*sin2x-√3/2cos2x)
=2(sin2xcosπ/3-cos2xsinπ/3)
=2sin(2x-π/3)
单调减区间：2kπ+π/2<=2x-π/3<=2kπ+π3/2
即：[5π/12+kπ,11π/12+kπ]
3sin^2x=(1-cos2a)/2
f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3
=2sinxcosx+2根号3*(1-cos2X)/2-根号3
=sin2X+根号3*(1-cos2X)-根号3
=sin2x+根号3-根号3cos2X-根号3
=sin2x-根号3cos2X
=2(1/2*sinx-根号3/2*c...
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3sin^2x=(1-cos2a)/2
f(x)=2sin(π-x)sin(π/2-x)+2根号3sin^2x-根号3
=2sinxcosx+2根号3*(1-cos2X)/2-根号3
=sin2X+根号3*(1-cos2X)-根号3
=sin2x+根号3-根号3cos2X-根号3
=sin2x-根号3cos2X
=2(1/2*sinx-根号3/2*cos2X)
=2(sin2x*cos60度-cos2X*sin60度)
=2sin(2X-60度)
=2sin(2X-派/3)
2K派+派/2<=2X-派/3<=2K派+3/2派
2K派+5派/6<=2X<=2K派+11派/6
所以,K派+5派/12<=X<=K派+11派1/12
所以,f(x)的单调递减区间为[K派+5派/12,K派+11派1/12]
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