已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b| 若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13求 sinα答案sinα=33/65跪求详细步骤~
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![已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b| 若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13求 sinα答案sinα=33/65跪求详细步骤~](/uploads/image/z/1812606-6-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos%CE%B1%2Csin%CE%B1%29+b%3D%28cos%CE%B2%2Csin%CE%B2%29+%7Ca%2Bb%7C%3D2%7Ca-b%7C+%E8%8B%A50%EF%BC%9C%CE%B1%EF%BC%9C%CF%80%2F2+++%2C-%CF%80%2F2+%EF%BC%9C%CE%B2%EF%BC%9C0+%2C%E4%B8%94sin%CE%B2%3D-5%2F13%E6%B1%82+sin%CE%B1%E7%AD%94%E6%A1%88sin%CE%B1%3D33%2F65%E8%B7%AA%E6%B1%82%E8%AF%A6%E7%BB%86%E6%AD%A5%E9%AA%A4%7E)
已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b| 若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13求 sinα答案sinα=33/65跪求详细步骤~
已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b|
若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13
求 sinα
答案sinα=33/65
跪求详细步骤~
已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b| 若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13求 sinα答案sinα=33/65跪求详细步骤~
已知向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b|
若0<α<π/2 ,-π/2 <β<0 ,且sinβ=-5/13
求 sinα
解析:∵向量a=(cosα,sinα) b=(cosβ,sinβ) |a+b|=2|a-b|
|a+b|=√[(cosα+cosβ)^2+(sinα+sinβ)^2] =√[2(1+cos(α-β))]
|a-b|=√[(cosα-cosβ)^2+(sinα-sinβ)^2] =√[2(1-cos(α-β))]
∴√[2(1+cos(α-β))]=2√[2(1-cos(α-β))]
cos(α-β)=3/5
∵0<α<π/2,-π/2 <β<0,sinβ=-5/13
Cosβ=12/13
12/13cosα-5/13sinα=3/5
与(cosα)^2+(sinα)^2=1联立
解得cosα=56/65,sinα=33/56
∴sinα=33/56
(cosa+cosb)^2+(sina+sinb)^2=4(cosa-cosb)^2+4(sina-sinb)^2
sinb=-5/13 cosb=12/13
39=60cosa-25sina
解得sina=33/65