What does the 'h' in the hyperbola equation mean?

[Quarlep]

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) what's the "h"in there I need help (you can look also 52 min)

 

[Mentallic]

The professor miswrote on the board, it should be

1=\cosh^2w-\sinh^2w

Where

\cosh{x} = \frac{e^x+e^{-x}}{2}

\sinh{x} = \frac{e^x-e^{-x}}{2}

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

\cosh^2w-\sinh^2w=1
versus
\cos^2w+\sin^2w=1

 

[Quarlep]

whats the "h" means there I need to lear hyperbolic geometry to learn it I guess

 

[Mentallic]

The h stands for hyperbolic.
The sine function is denoted by sin, and evaluating the sine of \pi is done by calculating \sin(\pi).
Similarly, the hyperbolic sine function is denoted by sinh and evaluating this function at x=5 is done by \sinh(5), except we can also represent the sinh function by
\sinh(x)=\frac{e^x-e^{-x}}{2}
hence
\sinh(5)=\frac{e^5-e^{-5}}{2}

 

[Quarlep]

I understand it thanks