sin+x+y
@长享1565：急:sin(x+y)=sinxcosy+cosxsiny怎么证明??? -
谈政18634687708…… 用三角函数的积化和差公式,sinXcosY=[sin(X+Y)+sin(X-Y)]/2 cosXsinY=[sin(X+Y)-sin(X-Y)]/2 两个式子一加,消去sin(X-Y)即可
@长享1565：请帮我证明sin(x+y)=sinxcosy+cosxsiny不要这种方法 要正常点的计算! - 作业帮
谈政18634687708…… [答案] sin(x+y)=sinxcosy+cosxsiny 具体推导: 首先建立直角坐标系,在直角坐标系xOy中作单位圆O,并作出角a,b,与-b,使角a的开边为Ox,交圆O于点P1,终边交圆O于点P2,角b的始边为OP2,终边交圆O于点P3,角-b的始边为OP1,终边交圆O于点...
@长享1565：sin(x+y)=sinxcosy+cosxsiny -
谈政18634687708…… 该公式是根据单位圆推导出来的,是基本公式,一般不用证明
@长享1565：证明sin(x+y)=sinx*cosy+cosx*siny的过程谁有这个的证明过程给法个谢谢. - 作业帮
谈政18634687708…… [答案] 推荐一种向量法证明: 在单位圆上取两点M N,与x轴的夹角分别是x,pi/2+y 则M(cosx,sinx),N(-siny,cosy) (OM,ON)= cos(OM,ON)=cos(pi/2+y-x)=sin(x-y)=OM点乘ON/(|OM||ON|) 即 sin(x-y)=sinxcosy-cosxsiny 用-y替换y可得:sin(x+y)=sinxcosy+cosxsiny ...
@长享1565：选择题sin(x+y)=sinx+siny,下面结论正确的是 -
谈政18634687708…… 解:sin(x+y)=sinxcosy+cosxsiny小于等于sinx+siny所以A是错的 当x+y=2kπ(k∈z)时,sin(x+y)=0,而sin(2kπ-x)=-sinx,即sinx+siny=sinx+sin(2kπ-x)=sinx-sinx=0,所以B是对的,则CD均错 所以本题选B
@长享1565：为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2 -
谈政18634687708…… x+y=x+y/2+y/2 x=x+y/2-y/2 sin(x+y)=sin(x+y/2+y/2)=sin(x+y/2)cosy/2+cos(x+y/2)siny/2 sinx=sin(x+y/2)cosy/2-cos(x+y/2)siny/2 所以 sin(x+y) - sinx =sin(x+y/2)cosy/2+cos(x+y/2)siny/2-[sin(x+y/2)cosy/2-cos(x+y/2)siny/2]= 2cos(x+y/2)siny/2
@长享1565：证明sin(x+y)=sinx*cosy+cosx*siny的过程 -
谈政18634687708…… 推荐一种向量法证明:在单位圆上取两点M N,与x轴的夹角分别是x,pi/2+y 则M(cosx,sinx),N(-siny,cosy) (OM,ON)= cos(OM,ON)=cos(pi/2+y-x)=sin(x-y)=OM点乘ON/(|OM||ON|) 即 sin(x-y)=sinxcosy-cosxsiny 用-y替换y可得:sin(x+y)=sinxcosy+cosxsiny 证毕 类似的可得到cos(x+y)的公式
@长享1565：求sin(x+y)=sinx+siny的导数 -
谈政18634687708…… 两边求导:cos(x+y)*(1+y')=cosx+cosy*y' y'=(cosx-cos(x+y))/(cos(x+y)-cosy) e^x+1=e^y*y'+y' y'=(e^x+1)/(e^y+1)
@长享1565：求sin(x+y)的二重积分,x,y均[0,pai/2] - 作业帮
谈政18634687708…… [答案] 化成sin(x+y)=sinxcosy+cosxsiny计算.
@长享1565：y'+sin(x+y)=sin(x - y)的通解 -
谈政18634687708…… y'=sin(x-y)-sin(x+y)=-2cosxsiny, ∴dy/siny=-2cosxdx, 积分得zdlntan(y/2)=-2sinx+C', tan(y/2)=Ce^回(-2sinx), y/2=kπ+arctan[Ce^(-2sinx)],k∈答Z, y=2kπ+2arctan[Ce^(-2sinx)],为所求.
谈政18634687708…… 用三角函数的积化和差公式,sinXcosY=[sin(X+Y)+sin(X-Y)]/2 cosXsinY=[sin(X+Y)-sin(X-Y)]/2 两个式子一加,消去sin(X-Y)即可
@长享1565：请帮我证明sin(x+y)=sinxcosy+cosxsiny不要这种方法 要正常点的计算! - 作业帮
谈政18634687708…… [答案] sin(x+y)=sinxcosy+cosxsiny 具体推导: 首先建立直角坐标系,在直角坐标系xOy中作单位圆O,并作出角a,b,与-b,使角a的开边为Ox,交圆O于点P1,终边交圆O于点P2,角b的始边为OP2,终边交圆O于点P3,角-b的始边为OP1,终边交圆O于点...
@长享1565：sin(x+y)=sinxcosy+cosxsiny -
谈政18634687708…… 该公式是根据单位圆推导出来的,是基本公式,一般不用证明
@长享1565：证明sin(x+y)=sinx*cosy+cosx*siny的过程谁有这个的证明过程给法个谢谢. - 作业帮
谈政18634687708…… [答案] 推荐一种向量法证明: 在单位圆上取两点M N,与x轴的夹角分别是x,pi/2+y 则M(cosx,sinx),N(-siny,cosy) (OM,ON)= cos(OM,ON)=cos(pi/2+y-x)=sin(x-y)=OM点乘ON/(|OM||ON|) 即 sin(x-y)=sinxcosy-cosxsiny 用-y替换y可得:sin(x+y)=sinxcosy+cosxsiny ...
@长享1565：选择题sin(x+y)=sinx+siny,下面结论正确的是 -
谈政18634687708…… 解:sin(x+y)=sinxcosy+cosxsiny小于等于sinx+siny所以A是错的 当x+y=2kπ(k∈z)时,sin(x+y)=0,而sin(2kπ-x)=-sinx,即sinx+siny=sinx+sin(2kπ-x)=sinx-sinx=0,所以B是对的,则CD均错 所以本题选B
@长享1565：为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2 -
谈政18634687708…… x+y=x+y/2+y/2 x=x+y/2-y/2 sin(x+y)=sin(x+y/2+y/2)=sin(x+y/2)cosy/2+cos(x+y/2)siny/2 sinx=sin(x+y/2)cosy/2-cos(x+y/2)siny/2 所以 sin(x+y) - sinx =sin(x+y/2)cosy/2+cos(x+y/2)siny/2-[sin(x+y/2)cosy/2-cos(x+y/2)siny/2]= 2cos(x+y/2)siny/2
@长享1565：证明sin(x+y)=sinx*cosy+cosx*siny的过程 -
谈政18634687708…… 推荐一种向量法证明:在单位圆上取两点M N,与x轴的夹角分别是x,pi/2+y 则M(cosx,sinx),N(-siny,cosy) (OM,ON)= cos(OM,ON)=cos(pi/2+y-x)=sin(x-y)=OM点乘ON/(|OM||ON|) 即 sin(x-y)=sinxcosy-cosxsiny 用-y替换y可得:sin(x+y)=sinxcosy+cosxsiny 证毕 类似的可得到cos(x+y)的公式
@长享1565：求sin(x+y)=sinx+siny的导数 -
谈政18634687708…… 两边求导:cos(x+y)*(1+y')=cosx+cosy*y' y'=(cosx-cos(x+y))/(cos(x+y)-cosy) e^x+1=e^y*y'+y' y'=(e^x+1)/(e^y+1)
@长享1565：求sin(x+y)的二重积分,x,y均[0,pai/2] - 作业帮
谈政18634687708…… [答案] 化成sin(x+y)=sinxcosy+cosxsiny计算.
@长享1565：y'+sin(x+y)=sin(x - y)的通解 -
谈政18634687708…… y'=sin(x-y)-sin(x+y)=-2cosxsiny, ∴dy/siny=-2cosxdx, 积分得zdlntan(y/2)=-2sinx+C', tan(y/2)=Ce^回(-2sinx), y/2=kπ+arctan[Ce^(-2sinx)],k∈答Z, y=2kπ+2arctan[Ce^(-2sinx)],为所求.
