Results 1 to 4 of 4

Math Help - Derivation of Law of Cosines (excerpt)

  1. #1
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432

    Derivation of Law of Cosines (excerpt)

    Prove that a=b \cos{C}+c \cos{B}

    I have that
    \cos{C}=\frac{x}{b} \implies x=b \cos{C}

    \cos{B}=\frac{a+x}{c} \implies x=c \cos{B}-a

    Hence,

    a=c \cos{B}-b\cos{C}

    A difference instead of a sum??
    Attached Thumbnails Attached Thumbnails Derivation of Law of Cosines (excerpt)-untitled2.jpg  
    Last edited by DivideBy0; August 21st 2007 at 02:57 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    You are using  \cos (\angle C) in two different ways.
    Note that \cos (\angle BCA) =  - \cos (\angle DCA).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Oooh, thanks...

    You're using cos(180-\theta) = -cos(\theta) right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    You can use the sines law.
    We have b=2R\sin B, c=2R\sin C.
    We start from the right member:
    b\cos C+c\cos B=2R\sin B\cos C+2R\sin C\cos B=
    =2R(\sin B\cos C+\sin C\cos B)=
    =2R\sin(B+C)=
    =2R\sin(180-A)=
    =2R\sin A=
    =a
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivation and Jordan derivation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 8th 2011, 09:22 PM
  2. Law of Cosines, help!
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 19th 2009, 06:18 AM
  3. Replies: 5
    Last Post: July 26th 2008, 11:13 PM
  4. The law of cosines
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 21st 2008, 12:38 PM
  5. Law of Cosines Derivation
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 23rd 2008, 12:58 PM

Search Tags


/mathhelpforum @mathhelpforum