Calculating Equation of Evolute for Catenary Curve

[T-O7]

Ok, so i need to calculate the equation of the evolute for the catenary
$$\gamma(t)= (t,cosh(t))$$.
I'm not really sure how to do this, the definition of evolute I have requires a unit-speed parametrization, but it looks a little difficult to find that also (the arclength if I'm correct is given by
$$s(t)=\frac{1}{2}(sin(2t)+t)$$).

Is there some "standard" way of finding the evolute?

 

[HallsofIvy]

You are NOT correct about the arclength (did you confuse cosh(t) with cos(t)?).

if $\gamma(t)= (t, cosh(t))$ then the arclength is given by [tex]\integral\sqrt{1+ sinh^2(t)}dt= \integral cosh(t)dt= sinh(t)[/itex].[/tex]

 

[T-O7]

Yeah, i made a boo boo calculating the arclength . And apparently the definition i was given for the evolute of a unit-speed curve can also be used for any other parametrization of the curve, so everything's a-okay.