已知向量A=(2cosa ,-2sina )a∈(π/2,π),b=(0,1),则向量a与b的夹角是
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 16:30:15
![已知向量A=(2cosa ,-2sina )a∈(π/2,π),b=(0,1),则向量a与b的夹角是](/uploads/image/z/8837741-29-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8FA%3D%282cosa+%2C-2sina+%29a%E2%88%88%28%CF%80%2F2%2C%CF%80%29%2Cb%3D%280%2C1%29%2C%E5%88%99%E5%90%91%E9%87%8Fa%E4%B8%8Eb%E7%9A%84%E5%A4%B9%E8%A7%92%E6%98%AF)
已知向量A=(2cosa ,-2sina )a∈(π/2,π),b=(0,1),则向量a与b的夹角是
已知向量A=(2cosa ,-2sina )a∈(π/2,π),b=(0,1),则向量a与b的夹角是
已知向量A=(2cosa ,-2sina )a∈(π/2,π),b=(0,1),则向量a与b的夹角是
a=(2cosα,-2sinα),则:|a|=2
b=(0,1),即:|b|=1
a·b=-2sinα,故:cos=a·b/(|a|*|b|)
=-2sinα/2=-sinα=sin(-α)=cos(π/2+α)
=cos(-π/2-α)=cos(2π-π/2-α)=cos(3π/2-α)
α∈(π/2,π),故:3π/2-α∈(π/2,π)
故:=3π/2-α