已知向量a=(cosa,sina),b =(cosb .sinb),且|a -b|=(2根号5)/5
问题描述:
已知向量a=(cosa,sina),b =(cosb .sinb),且|a -b|=(2根号5)/5
1、求cos(a-b )的值 2、若0<a <派/2,-派/2<b <0,且sinb=-5/13.求sin a
答
a-b=((cosa-cosb),(sina-sinb))
|a-b|^2=(cosa-cosb)^2+(sina-sinb)^2=(2√5/5)^2=4/5
2-2cos(a-b)=4/5
cos(a-b)=3/5
0