# Reparametrization of tractrix

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• November 7th 2011, 05:26 AM
HAL9000
Reparametrization of tractrix
Hello!

I wonder how to choose a reparametrization map, so that I can transfrom the curve given by

$c_1(t)=(\sin t, \cos t + \ln \tan (t/2))$

to

$c_2(t)=(\frac{1}{\cosh t},t-\tanh t)$

...and vice versa.

Can't see it at the moment.
Any ideas?

Thanks in advance
• November 7th 2011, 10:20 AM
FernandoRevilla
Re: Reparametrization of tractrix
For example, if $t=\arcsin \left(\frac{1}{\cosh u}\right)$ , then $\cos t=\ldots=\pm \tanh u$ etc .