Angle between catenary and line

  • Thread starter flash
  • Start date
  • #1
flash
68
0

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
Science Advisor
Homework Helper
43,021
970
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.
 

Suggested for: Angle between catenary and line

  • Last Post
Replies
7
Views
168
  • Last Post
Replies
12
Views
143
  • Last Post
Replies
4
Views
39
Replies
15
Views
205
Replies
2
Views
263
  • Last Post
Replies
2
Views
267
Replies
4
Views
574
Replies
6
Views
271
Top