Turn on thread page Beta
    • Thread Starter

    I've not really been educated on the applications of hyperbolic trig functions (i.e. cosh(x), sinh(x)). Could anyone help me out?
    • Community Assistant

    Community Assistant
    Here are a few applications:

    The curve y = \cosh x is a catenary. Google it to find out about hanging chains and bridge archs.

    The hyperbolic functions are connected to the trigonometric functions via complex numbers.

    Alternatively, Google the Gudermannian function to find a direct connection between trigonometric and hyperbolic numbers. There is an interesting application here in the Mercator projection of the world map.

    Vincenzo Riccati introduced the hyperbolic functions to solve cubic equations so there is another application there.

    The rapidity of an object in special relativity is given by the formula \phi = \tanh^{-1} \frac{v}{c}.

    The inverse sinh function is used to calculate the Roche Limit, the minimum distance at which a natural satellite may orbit a planet without being torn apart by tidal forces.

    Many expressions involving the sum or difference of two squares can be integrated by making a hyperbolic substitution.

    The parametric equations of the right hand branch of the unit rectangular hyperbola x^2 -y^2 =1 are x = \cosh t and y=\sinh t.
Submit reply
Turn on thread page Beta
Updated: February 9, 2010

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
How are you feeling in the run-up to Results Day 2018?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.