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Hyperbolic functions at x

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data
    find all other hyperbolic function at x for tanhx=12/13


    2. Relevant equations
    tanhx = sinhx/coshx
    cothx=1/tanhx
    etc...


    3. The attempt at a solution
    the only thing i got is cothx=13/12
    all i need to know is how to find sinhx and i will be fine.
     
  2. jcsd
  3. Nov 8, 2009 #2
    Why not solve for x and then evaluate sinh(x)?
     
  4. Nov 8, 2009 #3
    so x= tanh-1(12/13) ?
    then plug it in sinh(x)?

    i am not sure if i get it..
     
  5. Nov 8, 2009 #4

    Dick

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    tanh(x)=sinh(x)/cosh(x)=12/13. cosh(x)^2-sinh(x)^2=1. That's two equations in two unknowns. Can you find the solution?
     
  6. Nov 9, 2009 #5
    [tex]\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x} + 1}} = \frac{12}{13}[/tex]
    You can solve for x then plug it into the other hyperbolic trig functions. Or try what Dick suggested, looks like it should be easier.
     
  7. Nov 9, 2009 #6
    yeah i asked a teacher today too and he explained the same thing.
    that makes sense.

    even though, tanhx = sinhx/coshx = 12/13 then from here i could use sinhx =12 and coshx = 13 right away..
    but thats "the cheating way" i guess..

    thanks for help!
     
  8. Nov 9, 2009 #7

    Dick

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    sinh(x)=12 and cosh(x)=13 isn't only the 'cheating way', it's the wrong way. 13^2-12^2 isn't equal to 1.
     
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