余弦定理是怎么证明的如题``要详细点哦``最好有式子
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余弦定理是怎么证明的
如题``要详细点哦``最好有式子
如题``要详细点哦``最好有式子
![余弦定理是怎么证明的如题``要详细点哦``最好有式子](/uploads/image/z/18530087-23-7.jpg?t=%E4%BD%99%E5%BC%A6%E5%AE%9A%E7%90%86%E6%98%AF%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E7%9A%84%E5%A6%82%E9%A2%98%60%60%E8%A6%81%E8%AF%A6%E7%BB%86%E7%82%B9%E5%93%A6%60%60%E6%9C%80%E5%A5%BD%E6%9C%89%E5%BC%8F%E5%AD%90)
△ABC的AC=b,CB=a,AB=c,则A,B,C点的坐分别为A(b,0),B(acos C,asin C),C(0,0).
∠ACB=∠C,CB为∠ACB的终边,B为CB上一点,设B的坐标为(x,y),则sinC= =,cos C==所以B点坐标x=acosC,y=asinC.
|AB|2=(acosC-b)2+(asinC-0)2
=a2cos2C-2abcosC+b2-a2sin2C
=a2+b2-2abcos C,
即c2=a2+b2-2abcos C.
证明2:参考http://www.pkuschool.com/zadmin/manage/details.asp?TopicAbb=directions&FileName=g1v4sxb5570a05.htm
∠ACB=∠C,CB为∠ACB的终边,B为CB上一点,设B的坐标为(x,y),则sinC= =,cos C==所以B点坐标x=acosC,y=asinC.
|AB|2=(acosC-b)2+(asinC-0)2
=a2cos2C-2abcosC+b2-a2sin2C
=a2+b2-2abcos C,
即c2=a2+b2-2abcos C.
证明2:参考http://www.pkuschool.com/zadmin/manage/details.asp?TopicAbb=directions&FileName=g1v4sxb5570a05.htm