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

    14
    ReputationRep:
    There are often questions in paper asking to solve hyperbolic equation.






    This is the formula book :


    If you look in top example, there are two solutions to cosh(x) = 3, plus and minus. In another paper 2nd picture, there is only one solution to each sinh(x) hyperbolic equation. Why do they sometimes have plus and minus, formula doesn't say plus or minus, so where does that come work?
    Offline

    1
    ReputationRep:
    The cosh(x) graph is a many to one graph, so there is two solutions when solving. The sinh(x) graph is a one to one graph and so there is only one solution.
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    It's kinda like an y=x3 graph always having 1 solution for one input while the y=x2 graph always has 2 inputs and one solution. Using these graphs in particular as they have a similar shape to the cosh(x) and sinh(x) graphs
    Offline

    22
    ReputationRep:
    (Original post by Bealzibub)
    ...
    Look at the graphs of cosh and sinh. You'll see that cosh lacks injectivity whilst sinh is perfectly injective.
 
 
 
  • 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
    Are unpaid trial work shifts fair?
    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

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