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Solve for a constant in an equation

  1. Jan 14, 2016 #1
    Im trying to solve for a constant in an equation and it involves taking the arctanh(6.55) and my calculator is giving me an error, is there a way around this?
  2. jcsd
  3. Jan 14, 2016 #2

    H Smith 94

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    Gold Member

    Perhaps you could make use of $$\tanh(x) = \frac{\sinh(x)}{\cosh(x)} = \frac{e^x - e^{-x} }{ e^x + e^{-x} },$$ or $$\mathrm{arctanh}(x) = \frac{1}{2}\,\ln\left|\frac{1+x}{1-x} \right|.$$ These are all available by Googling "Hyperbolic trig identities".

    Also, you should probably mention what the equation is.
    Last edited: Jan 14, 2016
  4. Jan 15, 2016 #3
    This helps, thanks a lot
  5. Jan 15, 2016 #4
    The values of tanh are between -1 and 1.
    What you are trying to do is like asking for arcsin(2).
    Of course you get an error.:)
  6. Jan 15, 2016 #5


    Staff: Mentor

    If you let x = arctanh(6.55), an equivalent equation is tanh(x) = 6.55.

    Assuming that we're dealing only with real numbers, the range of the tanh function is ##-1 < \tanh(x) < 1##. This means that there is no real number x for which tanh(x) = 6.55, or equivalently, for which x = arctanh(6.55). That's what your calculator is telling you.

    Your calculator probably has some documentation about the values that can be used as arguments to each of the calculator's functions.

    Edit: nasu beat me by 2 minutes!
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