Results 1 to 2 of 2

Math Help - trigonometry system of equation

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    38

    trigonometry system of equation

    a, b, and c are known and greater than zero, solve for theta and phi from the two equations i) and ii).
    i)a*cos(theta) = b*cos(phi)
    ii)a*sin(theta) + b*sin(phi) = c

    thanks,
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,907
    Thanks
    765
    Hello, n0083!

    The problem is not difficult . . . The answers are ugly!



    a, b, c are known and greater than zero. .Solve for \theta and \phi

    . . \begin{array}{cccc} a\cos(\theta) &=& b\cos(\phi) & {\color{blue}[1]} \\ a\sin(\theta) &=& c -  b\sin(\phi) & {\color{blue}[2]}\end{array}

    \begin{array}{ccccc}\text{Square {\color{blue}[1]}:} & a^2\cos^2\!\theta &=& b^2\cos^2\!\phi \\<br /> <br />
 \text{Square {\color{blue}[2]}:} & a^2\sin^2\!\theta &=& c^2 - 2bc\sin\phi + b^2\sin^2\!\phi \end{array}

    \text{Add: }\;a^2\underbrace{(\sin^2\!\theta+\cos^2\!\theta)}  _{\text{This is 1}} \;=\;c^2 -2bc\sin\phi + b^2\underbrace{(\sin^2\phi + \cos^2\!\phi)}_{\text{This is 1}}

    . . a^2\;=\;c^2 - 2bc\sin\phi + b^2 \quad\Rightarrow\quad\sin\phi \;=\;\frac{b^2+c^2-a^2}{2bc} .[3]

    Hence: . \boxed{\phi \;=\;\sin^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)}


    Substitute [3] into [2] and solve for \sin(\theta) . . . then solve for \theta.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 2nd 2009, 09:06 AM
  2. trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 3rd 2008, 04:29 PM
  3. trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 1st 2007, 06:20 AM
  4. trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 15th 2007, 12:02 PM
  5. trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 11th 2007, 07:15 AM

Search Tags


/mathhelpforum @mathhelpforum