已知A向量(2,0)B向量(0,2)C向量(cosθ,sinθ)(1)若AC向量垂直BC向量,求sin2θ的值(2)OA向量+OC向量的模=根号7,且θ属于(0,派尔)求OB向量和OC向量的夹角
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 16:53:44
![已知A向量(2,0)B向量(0,2)C向量(cosθ,sinθ)(1)若AC向量垂直BC向量,求sin2θ的值(2)OA向量+OC向量的模=根号7,且θ属于(0,派尔)求OB向量和OC向量的夹角](/uploads/image/z/6730655-23-5.jpg?t=%E5%B7%B2%E7%9F%A5A%E5%90%91%E9%87%8F%EF%BC%882%2C0%EF%BC%89B%E5%90%91%E9%87%8F%EF%BC%880%2C2%EF%BC%89C%E5%90%91%E9%87%8F%EF%BC%88cos%CE%B8%2Csin%CE%B8%EF%BC%89%EF%BC%881%EF%BC%89%E8%8B%A5AC%E5%90%91%E9%87%8F%E5%9E%82%E7%9B%B4BC%E5%90%91%E9%87%8F%2C%E6%B1%82sin2%CE%B8%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89OA%E5%90%91%E9%87%8F%2BOC%E5%90%91%E9%87%8F%E7%9A%84%E6%A8%A1%3D%E6%A0%B9%E5%8F%B77%2C%E4%B8%94%CE%B8%E5%B1%9E%E4%BA%8E%EF%BC%880%2C%E6%B4%BE%E5%B0%94%EF%BC%89%E6%B1%82OB%E5%90%91%E9%87%8F%E5%92%8COC%E5%90%91%E9%87%8F%E7%9A%84%E5%A4%B9%E8%A7%92)
已知A向量(2,0)B向量(0,2)C向量(cosθ,sinθ)(1)若AC向量垂直BC向量,求sin2θ的值(2)OA向量+OC向量的模=根号7,且θ属于(0,派尔)求OB向量和OC向量的夹角
已知A向量(2,0)B向量(0,2)C向量(cosθ,sinθ)(1)若AC向量垂直BC向量,求sin2θ的值
(2)OA向量+OC向量的模=根号7,且θ属于(0,派尔)求OB向量和OC向量的夹角
已知A向量(2,0)B向量(0,2)C向量(cosθ,sinθ)(1)若AC向量垂直BC向量,求sin2θ的值(2)OA向量+OC向量的模=根号7,且θ属于(0,派尔)求OB向量和OC向量的夹角
1.-3/4 x1x2*y1y2=0 用向量垂直方程代入
2.30度 cosθ次方+sinθ=1次方可约 求出 cosθ=1/2 C向量(1/2,根号三/2)(OC的值 注意θ范围 OB向量和OC向量的夹角可以求出来了
(1)
AC.BC =0
(OC-OA).(OC-OB) =0
(cosθ-2,sinθ).(cosθ,sinθ-2)=0
(cosθ)^2 -2cosθ + (sinθ)^2 - 2sinθ =0
1-2sinθ-2cosθ=0
(sinθ+cosθ)^2 =(1/2)^2
1+2sinθcosθ = 1/4
sin2θ = -3/...
全部展开
(1)
AC.BC =0
(OC-OA).(OC-OB) =0
(cosθ-2,sinθ).(cosθ,sinθ-2)=0
(cosθ)^2 -2cosθ + (sinθ)^2 - 2sinθ =0
1-2sinθ-2cosθ=0
(sinθ+cosθ)^2 =(1/2)^2
1+2sinθcosθ = 1/4
sin2θ = -3/4
(2)
|OA+OC|=√7 θ∈(0,π)
|(2+cosθ,sinθ)|^2 = 7
(2+cosθ)^2+(sinθ)^2 =7
4+4cosθ+1 =7
cosθ= 1/2
θ =π/3
let OB和OC的夹角=x
OB.OC = (0,2).(cosθ,sinθ)
|OB||OC|cosx = 2sinθ
2cosx = 2sin(π/3)
cosx = √3/2
x = π/6
OB和OC的夹角=π/6
收起