Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    15
    ReputationRep:
    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
    Offline

    20
    ReputationRep:
    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.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.