Hyperbola equation

257
4
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)
 

Mentallic

Homework Helper
3,797
94
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]
 
257
4
whats the "h" means there I need to lear hyperbolic geometry to learn it I guess
 
Last edited:

Mentallic

Homework Helper
3,797
94
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]
 
257
4
I understand it thanks
 

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