1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hyperbola equation

Tags:
  1. Mar 13, 2015 #1
    I am studying leonard susskind lectures and there I saw a hyperbola equation


    I didnt understand that equation what it means coshw or sinhw or total equation(In 49 minute) whats the "h"in there I need help (you can look also 52 min)
     
  2. jcsd
  3. Mar 13, 2015 #2

    Mentallic

    User Avatar
    Homework Helper

    The professor miswrote on the board, it should be

    [tex]1=\cosh^2w-\sinh^2w[/tex]

    Where

    [tex]\cosh{x} = \frac{e^x+e^{-x}}{2}[/tex]

    [tex]\sinh{x} = \frac{e^x-e^{-x}}{2}[/tex]

    They're represented in this way because they appear frequently and quite often have very similar properties to the usual cos and sin trig functions, such as

    [tex]\cosh^2w-\sinh^2w=1[/tex]
    versus
    [tex]\cos^2w+\sin^2w=1[/tex]
     
  4. Mar 13, 2015 #3
    whats the "h" means there I need to lear hyperbolic geometry to learn it I guess
     
    Last edited: Mar 13, 2015
  5. Mar 13, 2015 #4

    Mentallic

    User Avatar
    Homework Helper

    The h stands for hyperbolic.
    The sine function is denoted by sin, and evaluating the sine of [itex]\pi[/itex] is done by calculating [itex]\sin(\pi)[/itex].
    Similarly, the hyperbolic sine function is denoted by sinh and evaluating this function at x=5 is done by [itex]\sinh(5)[/itex], except we can also represent the sinh function by
    [tex]\sinh(x)=\frac{e^x-e^{-x}}{2}[/tex]
    hence
    [tex]\sinh(5)=\frac{e^5-e^{-5}}{2}[/tex]
     
  6. Mar 15, 2015 #5
    I understand it thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hyperbola equation
  1. Intersecting Hyperbola (Replies: 0)

  2. Hyperbola question (Replies: 3)

  3. Hyperbola question (Replies: 4)

  4. The hyperbola (Replies: 6)

Loading...