已知向量a=(cosa,sina),b=(cosb.sinb),且|a-b|=(2根号5)/51、求cos(a-b)的值2、若0＜a＜派/2,-派/2＜b＜0,且sinb=-5/13.求sina

Question

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

Answer 1

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