- #1

morrobay

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sinh x= e^x-e^-x/2

Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

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- Thread starter morrobay
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- #1

morrobay

Gold Member

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sinh x= e^x-e^-x/2

Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

- #2

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- #3

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cos *x* = (e^{ix} + e^{-ix})/2

sin*x* = (e^{ix} - e^{-ix})/2

sin

Simply remove the

- #4

morrobay

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That cosh (a) ,( a = area of hyperbolic sector of unit hyperbola )

is equal to the x coordinate.

see my thread starter: (https://www.physicsforums.com/showthread.php?t=336897 [Broken])

also linked below.

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- #5

morrobay

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That cosh (a) ,( a = area of hyperbolic sector of unit hyperbola )

is equal to the x coordinate.

see my thread starter: (https://www.physicsforums.com/showthread.php?t=336897 [Broken])

also linked below.

Whats up Doc ?

Last edited by a moderator:

- #6

HallsofIvy

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They are so called because is y is any function of x satisfying that differential equation, then y(x)= y(0)cos(x)+ y'(0) sin(x). That is, the coefficients in the linear combination are just y(0) and y'(0).

The fundamental solutions for y"- y= 0, at x= 0, are, similarly, cosh(x) and sinh(x).

Of course, e

- #7

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[tex]cosh^{2}(x)-sinh^{2}(x)=1[/tex]

while the trigonometric cosines and sines describe a very basic circle:

[tex]cos^{2}(x)+sin^{2}(x)=1[/tex]

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