The form of the lorentz transformations

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In a lecture on special relativity online, the form

[tex]x'=x\cosh{\omega}-ct\sinh{\omega}[/tex]

[tex]t'=-x\sinh{\omega}+ct\cosh{\omega}[/tex]

is used for the lorentz transformations, where the velocity is [tex]v=\frac{c\sinh{\omega}}{\cosh{\omega}}[/tex].

However, I'm wondering, couldn't you also do

[tex]x'=x\sec{\omega}-ct\tan{\omega}[/tex]

[tex]t'=-x\tan{\omega}+ct\sec{\omega}[/tex]

(or even the similar thing with [tex]\csc{\omega}[/tex] and [tex]\cot{\omega}[/tex])

With [tex]v=\frac{c\tan{\omega}}{\sec{\omega}}[/tex]

Since this also reproduces the lorentz transformations

Is there any advantage to using the hyperbolic functions instead?
 

bcrowell

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When you use the hyperbolic functions the parameter [itex]\omega[/itex], called the rapidity, becomes additive. See http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.3 [Broken] , subsection 2.3.1.
 
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Cool, thanks
 

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