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Homework Help: Angle between catenary and line

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the angle between the line x=7 and the catenary [tex]y=20\cosh{(\frac{x}{20})}-15[/tex]

    3. The attempt at a solution

    I found the tangent has gradient [tex]\sinh{(\frac{7}{20})}[/tex]

    Then I used [tex]\tan{\theta}=|\frac{1}{m}|[/tex]
    where [tex]m=\sinh{(\frac{7}{20})}[/tex]

    And evaluated using inverse tan on my calculator.

    I'm pretty sure we aren't meant to use a calculator though, so my question is can the inverse tan of that be evaluated manually somehow?

    Thanks
     
  2. jcsd
  3. Apr 27, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    If you "aren't meant to use a calculator" then give, as your answer,
    [tex]tan^{-1}(\frac{1}{sinh(7/20)})[/tex]
    There is no simple way to calculate a numerical solution.
     
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