Question

有几道数学题。请几位高手帮忙解决。都很简单的。

1：已知0<X<90°<Y<180，sinx=3/5,cos(X+Y)=-4/5。求sinY=？

Answer 1

0<X<90°
cosx=√(1-(sinx)^2)=√(1-(3/5)^2)=4/5
cos(X+Y)=cosxcosy-sinxsiny
=4/5cosy-3/5siny=-4/5
4cosy-3siny=-4
cosy=(3/4)sinx-1
代入
(cosy)^2+(siny)^2=1
((3/4)siny-1)^2+(siny)^2=1
(25/16)(siny)^2-(3/2)siny=0
siny=0或siny=24/25
因为<90°<Y<180
siny不等于0
所以siny=24/25

Answer 2

因为90°<Y<180所以sinY>0
cosx=4/5
cox(x+y)=cosxcosy-sinxsiny=-4/5
4cosy+4=3siny
与siny^2+cosy^2=1联立即可
注意sinY>0
best wish