已知向量a=(cosx,sinx),向量b=(cosy,siny),|a-b|=2*&5/5,
1、求cos(x-y)的值
2、若0
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人气:201 ℃ 时间:2020-04-14 16:36:54
解答
向量a=(cosx,sinx),向量b=(cosy,siny),
则a^2=1,b^2=1,
ab= cosx cosy+sinx siny=cos(x-y),
|a-b|=2√5/5,
平方得:|a-b|^2=4/5,
即a^2+b^2-2ab=4/5,
1+1-2 cos(x-y) =4/5,
cos(x-y) =3/5.
-π/2<y<0,且siny=-5/13,
则cosy=12/13.
0
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