Finding unit tagnet and normal vectors, can you see if i messed up? is curvature t?

[mr_coffee]

Hello everyone, I think i did this problem right, but I want to make sure sure. The directions are as fallows:
(a) find the unit tagent and unit normal vectors T(t) and N(t).
(b) Use Formula 9 to find curvature.
Note: formula 9 is the one i have on my paper: k(t) = |T'(t)|/|r'(t)|;
my curvature came out as 1/t, is it okay that it still has the variable t in it or was it supppose to be a real number? it is a function of t so i'm assuming its okay. here is the problem and work, if its too hard to read tell me and i'll try to rescan it, the work from the other side is showing through alittle :eek:
http://img138.imageshack.us/img138/1275/kurve6kg.jpg
Thanks!

[Tom Mattson]

I haven't cranked through it myself, but your procedure looks fine.


Note: formula 9 is the one i have on my paper: k(t) = |T'(t)|/|r'(t)|;
my curvature came out as 1/t, is it okay that it still has the variable t in it or was it supppose to be a real number?


It's OK. The fact that the curvature depends on the parameter is simply an indication of the fact that the curvature varies as you move along the curve. In other words, it simply indicates that you are not dealing with a circle (which has constant curvature).

[mr_coffee]

cool thanks!