Angle between catenary and line

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  • #1
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Homework Statement


Find the angle between the line x=7 and the catenary [tex]y=20\cosh{(\frac{x}{20})}-15[/tex]

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
 

Answers and Replies

  • #2
HallsofIvy
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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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