1,已只函数f(x)=2cosx(sinx-cosx)+1,x属于R (1)求函数f(x)的最小正周期.(2)求函数f(x)在区间[π/8,3/4π]上最小值和最大值2,已知sinx+siny=1/3,(1)求sinx的取值范围.(2)求a=siny-cos的平方x的最值
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![1,已只函数f(x)=2cosx(sinx-cosx)+1,x属于R (1)求函数f(x)的最小正周期.(2)求函数f(x)在区间[π/8,3/4π]上最小值和最大值2,已知sinx+siny=1/3,(1)求sinx的取值范围.(2)求a=siny-cos的平方x的最值](/uploads/image/z/10153895-23-5.jpg?t=1%2C%E5%B7%B2%E5%8F%AA%E5%87%BD%E6%95%B0f%28x%29%3D2cosx%28sinx-cosx%29%2B1%2Cx%E5%B1%9E%E4%BA%8ER+%281%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F.%EF%BC%882%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B%CF%80%2F8%2C3%2F4%CF%80%5D%E4%B8%8A%E6%9C%80%E5%B0%8F%E5%80%BC%E5%92%8C%E6%9C%80%E5%A4%A7%E5%80%BC2%2C%E5%B7%B2%E7%9F%A5sinx%2Bsiny%3D1%2F3%2C%281%29%E6%B1%82sinx%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.%EF%BC%882%EF%BC%89%E6%B1%82a%3Dsiny-cos%E7%9A%84%E5%B9%B3%E6%96%B9x%E7%9A%84%E6%9C%80%E5%80%BC)
1,已只函数f(x)=2cosx(sinx-cosx)+1,x属于R (1)求函数f(x)的最小正周期.(2)求函数f(x)在区间[π/8,3/4π]上最小值和最大值2,已知sinx+siny=1/3,(1)求sinx的取值范围.(2)求a=siny-cos的平方x的最值
1,已只函数f(x)=2cosx(sinx-cosx)+1,x属于R (1)求函数f(x)的最小正周期.(2)求函数f(x)在区间[π/8,3/4π]上最小值和最大值
2,已知sinx+siny=1/3,(1)求sinx的取值范围.(2)求a=siny-cos的平方x的最值
1,已只函数f(x)=2cosx(sinx-cosx)+1,x属于R (1)求函数f(x)的最小正周期.(2)求函数f(x)在区间[π/8,3/4π]上最小值和最大值2,已知sinx+siny=1/3,(1)求sinx的取值范围.(2)求a=siny-cos的平方x的最值
f(x)=2cosx(sinx-cosx)+1
=2sinxcos-2cosx^2+1
=sin2x-cos2x
=根号2*sin(2x-π/4)
T=2π/2=π
x∈[π/8,3π/4],2x-π/4∈[0,5π/4],
sin(2x-π/4)∈[-根号2/2,1】,
最小值为-1,最大值为根号2.
2.-1≤siny=1/3-sinx≤1,且-1≤sinx≤1
解得:-2/3≤sinx≤1
a=siny-(cosx)^2=1/3-sinx+(sinx)^2-1
=(sinx)^2-sinx-2/3
=(sinx-1/2)^2-11/12
当sinx=1/2时,最小值是-11/12
当sinx=-2/3时,最大值是4/9
1.
f(x)=2osx(sinx-cosx)+1=2sinx*cosx-2(cosx)^2+1=sin2x-cos2x
=根号2(sin2xcosπ/4-cos2xsinπ/4)=根号2sin(2x-π/4)
那么函数的最小正周期为π
在[π/8,3/4π]中,π/8<=x<=3/4π
π/4<=2x<=3/2π
0<=2x-π/4<=...
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1.
f(x)=2osx(sinx-cosx)+1=2sinx*cosx-2(cosx)^2+1=sin2x-cos2x
=根号2(sin2xcosπ/4-cos2xsinπ/4)=根号2sin(2x-π/4)
那么函数的最小正周期为π
在[π/8,3/4π]中,π/8<=x<=3/4π
π/4<=2x<=3/2π
0<=2x-π/4<=5/4π
那么在该区间最小值是0,最大值是根号2
2.由于sinx+siny=1/3,sinx=1/3-siny,由于siny的取值是[0,1],则
(1/3)-1<=sinx<=(1/3)+1,-2/3<=sinx<=4/3,由于sinx<=1,则
-2/3<=sinx<=1
由于-2/3<=sinx<=1
4/9<=(sinx)^2<=1
-1<=-(sinx)^2<=-4/9
1-1<=1-(sinx)^2<=1-4/9
0<=(cosx)^2<=5/9
-5/9<=(cosx)^2<=0
而-1<=siny<=1,那么
-1-5/9<=siny-(cosx)^2<=1+0
-14/9<=siny-(cosx)^2<=1
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