Need some help with a Cal 3 question.?

Posted on 2016-12-05 18:49:00 in Math by NATHAN

I am currently studying for finals and I am trying to figure out how to go about fully solving this problem. I need to find T, N and k of a space curve r(t) = cos^3(t)i+sin^3(t)j. Now I am pretty sure I have the tangent and normal vectors, as well as the curvature. My issue is that the problem also gives the parameters 0<t<pi/2 (the less than signs are less than or equal to). 

Currently T, N and k I have: 
T(t) = [2sin^2(t)cos(t) - 3cos^2(t)sin(t)] / sin(2t) 
N(t) = -T(t) (I found that |T'| was equal to -1) 
k(t) = -2 / 3sin^2(t) 

First off, are those correct? Second, how does the parameter come into play? Am I supposed to use that to find the arc length of r(t) from 0 to pi/2? Or am I supposed to use that with k(t) or one of the other functions, and find the integral?

---

Answer Comment

No Answers Posted Yet.