I am doing a TNB-Frame problem and I am currently finding the tangent. The point I am trying to find it at is t=0 and my vector T(t) comes out to be in indeterminate form. So my question is how would I solve for vector T(t).

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- Mar 28th 2010, 02:04 PMSgraveyardVector Calculus
I am doing a TNB-Frame problem and I am currently finding the tangent. The point I am trying to find it at is t=0 and my vector T(t) comes out to be in indeterminate form. So my question is how would I solve for vector T(t).

- Mar 28th 2010, 02:11 PMcraig
- Mar 28th 2010, 02:13 PMSgraveyard
Vector T(t) = <tcos(t), tsin(t),0>/sqrt(t^2*cos^2(t)+t^2*sin^2(t))

At t=0

R(t) was originally <cos(t)+t*sin(t),sin(t)-t*cos(t),1> - Mar 28th 2010, 02:18 PMcraig
- Mar 28th 2010, 02:22 PMSgraveyard
- Mar 28th 2010, 02:25 PMcraig
So is it the vector $\displaystyle T(t) = (t\cos(t), t\sin(t),0>$ that you want to differentiate?

- Mar 28th 2010, 02:29 PMSgraveyard
Nah. I differentiated $\displaystyle R(t)= <cos(t)+t*sin(t),sin(t)-t*cos(t),1>$ into $\displaystyle R'(t)=<t*cos(t),t*sin(t),0>$

My goal is to find vector T(t) which is $\displaystyle R'(t)'/|R'(t)|$

When you do that though you are in indeterminate form. So my question is how would I solve it properly? - Mar 28th 2010, 02:31 PMcraig
- Mar 28th 2010, 02:34 PMSgraveyard