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Math Help - hyperbolic

  1. #1
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    hyperbolic

    how do you solve this simultaneous equations?

    sinh x + sinh y = 25/12
    cosh x - cosh y = 5/12
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do you solve this simultaneous equations?

    sinh x + sinh y = 25/12
    cosh x - cosh y = 5/12
    You could try writing \sin, \cos, \sinh, \cosh in their exponential form.

    \sinh{x} = \frac{e^{x}-e^{-x}}{2}

    \cosh{x} = \frac{e^{x}+e^{-x}}{2}

    \sin{x} = \frac{e^{ix}-e^{-ix}}{2i}

    \cos{x} = \frac{e^{ix}+e^{-ix}}{2}

    If you then multiply your second equation by 5 then you can set the two equal to one another.

    I should just add that i is a constant where i = \sqrt{-1}
    Last edited by mr fantastic; November 12th 2009 at 03:50 AM. Reason: Merged posts
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  3. #3
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    having using your mtd, i ended up with 2e^x + 2 e^-x = 3e^y -2e^y.

    i tried to let e^x = a and e^y =b and then i got

    2a + 2(1/a) = 3( b) - 2(1/b)

    solving a as a quadratic eqn, i got a and b to be complex numbers..

    which according to my notes, it is wrong as the answer should be real values.

    did i do sth wrong?
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    how do you solve this simultaneous equations?

    sinh x + sinh y = 25/12
    cosh x - cosh y = 5/12
    Solve the following simultaneously:

    a + b = \frac{25}{12} .... (1)

    c - d = \frac{5}{12} .... (2)

    c^2 - a^2 = 1 .... (3)


    d^2 - b^2 = 1 .... (4)
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