已知向量a=(cosX,sinX),b=(cosY,sinY),|a-b|=5分之2根号5.若0<X<π/2,-π/2<Y<0,且sinY= -5/13,求sinX?

问题描述:

已知向量a=(cosX,sinX),b=(cosY,sinY),|a-b|=5分之2根号5.若0<X<π/2,-π/2<Y<0,
且sinY= -5/13,求sinX?

-π/2<Y<0,sinY=-5/13,则cosY=12/13(a-b)2=a2+b2-2ab=2-2cos(X+Y)(a-b)2=4/5cos(X+Y)=3/5sin(X+Y)=-4/5或4/5sinX=sin(X+Y-Y)=sin(X+Y)cosY-cos(X+Y)sinY=63/65或-33/65(舍去),因为0<X<π/2,si...