搜搜考试网y=3sin(pai 3-x)
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sinx的周期是2pai,sin3x的周期是三分之二pai,sin5x的周期是五分之二pai取其最小公倍数,则y的周期是2pai.
sin(x+y)sin(x-y)=-1/2(cos(x+y+x-y)—cos(x+y-x+y))=-1/2(cos2x—cos2y)=-1/2(1-2（sinx）^2-1+2(siny）^2)=（si
你用积化和差公式一套,然后就能看出它的最小正周期来的.应该是1pi
y=sin^3x是复合函数可以设t=sinxt'=cosxy=t^3y'=3t^2*t'y'=3sin^2x*cosx
左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)=sin²xcos²y-cos²xsin²y=sin²x(1-sin
再答：希望采纳！谢谢
y'sin(y/x)-y/x*sin(y/x)+1=0令y/x=u,则y'=u+xu'所以(u+xu')sinu-usinu+1=0xu'sinu+1=0-sinudu=dx/x两边积分：cosu=l
y'=(cos²x)'-(sin3^x)'=2cosx·(cosx)'-cos3^x·(3^x)'=2cosx·(-sinx)-cos3^x·(3^x·ln3)=-sin2x-ln3·cos
sin^2x+cos^2y=1/2∴sin^2x=1/2-cos^2y3sin^2x+sin^2y=3（1/2-cos^2y）+sin^2y=1.5-3cos^2y）+sin^2y又有sin^2y+c
(x^x)'=(1+lnx)x^x所以y'=(1+lnx)x^xcos(x^x)
sinx+siny+sinz-sin(x+y+z)=4sin[(x+y)/2]sin[(x+z)/2]sin[(y+z)/2]sinx+siny+sinz-sin(x+y+z)=2sin[(x+y)/
y=sin(x+π/3)sin(x+π/2)=sin(x+π/3)cosx=(sinxcosπ/3+cosxsinπ/3)cosx=1/2sinxcosx+√3/2cos^2(x)[cos^2(x)指
Sinx-siny=2/3cosx-cosy=1/2分别平方得(Sinx-siny)^2=(2/3)^2(cosx-cosy)^2=(1/2)^2展开相加得-2cos(x-y)+2=4/9+1/4-2
由题意x∈[0，π2]，得x+π3∈[π3，5π6]，∴sin（x+π3）∈[12，1]∴函数y=sin（x+π3）在区间[0，π2]的最小值为12故答案为12
y=3sin(x+20°)+5sin(x+80°）=3sin(x+20°)+5sin(x+20°+60°）=3sin(x+20°)+5*[sin(x+20°)*cos60°+cos(x+20°)*si
y=sin²x+2sinxcosx+3cos²xy=(sin²x+cos²x)+2sinxcosx+(2cos²x-1)+1=1+sin2x+cos2
y=3^[sin(1/x)]y'=3^[sin(1/x)]ln3*cos(1/x)*(-1/x^2)=-ln3*3^[sin(1/x)]*cos(1/x)/x^2
dy/d(x^3)=(dy/dx)/(d(x^3)/dx)=cosx/3(x^2)