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Hyperbola equation

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  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

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    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

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    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
     
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