# Math Help - Reparametrization of tractrix

1. ## 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

2. ## Re: Reparametrization of tractrix

For example, if $t=\arcsin \left(\frac{1}{\cosh u}\right)$ , then $\cos t=\ldots=\pm \tanh u$ etc .