Y=2sinX(sinX-cosX)1 最小正周期2 單調(diào)區(qū)間

熱心網(wǎng)友

解：Y=2sinX(sinX-cosX)=2(sinX)^2-2sinXcosX=1-cos2X-sin2X=1-(√2)[sin(π/4)cos2X+cos(π/4)sin2X]=1-(√2)sin(π/4+2X)所以，Y=2sinX(sinX-cosX) 的最小正周期為2π/2=π.因?yàn)閟in(π/4+2X)在2nπ-π/2≤π/4+2X≤2nπ+π/2,(n為整數(shù),以下同)即nπ-3π/8≤X≤nπ+π/8時(shí)，單調(diào)增加,在2nπ+π/2≤π/4+2X≤2nπ+3π/2,即nπ+π/8≤X≤nπ+5π/8時(shí)，單調(diào)減少，所以，-(√2)sin(π/4+2X)在nπ-3π/8≤X≤nπ+π/8時(shí)，單調(diào)減少,在nπ+π/8≤X≤nπ+5π/8時(shí)，單調(diào)增加.所以，Y=2sinX(sinX-cosX)的單調(diào)區(qū)間為[nπ-3π/8,nπ+5π/8].

熱心網(wǎng)友

Y=2sinX(sinX-cosX)1 最小正周期2 單調(diào)區(qū)間

熱心網(wǎng)友

y=2sinx(sinx-cosx)=2(sinx)^2-2sinxcosx=1-cos2x-sin2x=1-(√2)sin[2x+(π/4)]即y=1-(√2)sin[2x+(π/4)]最小正周期T=2π/2=π 單調(diào)減少區(qū)間：2kπ-π/2≤2x+(π/4)≤2kπ+π/2即：kπ-3π/8≤x≤kπ+π/8 k∈Z 單調(diào)增加區(qū)間：2kπ+π/2≤2x+(π/4)≤2kπ+3π/2即：kπ+π/8≤x≤kπ+5π/8 k∈Z

熱心網(wǎng)友

y=2sinx(sinx-cosx)=2(snx)^2-2sinxcosx=(1-cos2x)-sin2x=1-(sin2x+con2x)=1-(√2)sin(2x+pi/4)1.周期T=(2pi)/2=pi2.因?yàn)?sinx在區(qū)間[2kpi-pi/2,2kpi+pi/2]內(nèi)是減函數(shù),在[2kpi+pi/2,2kpi+3pi/2]內(nèi)是增函數(shù).(k是整數(shù),下同)因此,由2kpi-pi/2=<2x+pi/4=<2kpi+pi/2 ;2kpi+pi/2=<2x+pi/4=<2kpi+3pi/2解得kpi-3pi/8=