Thread: Finding unit speed reparametrisations of regular curves

How can i find unit speed reparametrisations of these regular curves?

1) y(t) = (cos^2(t),sin^2(t)) -infinity < t < infinity (cos squared t, sine squared t)

2) y(t) = (t, cosh(t) -infinity < t < infinity

thanks

Originally Posted by millwallcrazy

How can i find unit speed reparametrisations of these regular curves?

1) y(t) = (cos^2(t),sin^2(t)) -infinity < t < infinity (cos squared t, sine squared t)

2) y(t) = (t, cosh(t) -infinity < t < infinity

I'll show how to do 2). Then you try 1). (Though why someone from Leeds should want to help a Millwall fan I can't imagine. )

In 2), the coordinates are x=t, y=cosh(t). The arc length is given by . The inverse function is given by , and the unit speed parametrisation (with parameter u) is given by

.