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Math Help - Vector Calculus

  1. #1
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    Vector 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).
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  2. #2
    Super Member craig's Avatar
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    Quote Originally Posted by Sgraveyard View Post
    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).
    People will be able to help easier if you post your question, and the work you have done so far.
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  3. #3
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    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>
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  4. #4
    Super Member craig's Avatar
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    Quote Originally Posted by Sgraveyard View Post
    Vector T(t) = <tcos(t), tsin(t),0>/sqrt(t^2*cos^2(t)+t^2*sin^2(t))

    At t=0
    You need to wrap your latex in MATH codes.

    Is your vector T(t) = (t\cos(t), t\sin(t),0>, not sure what the \sqrt{t^2*cos^2(t)+t^2*sin^2(t)} is?
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    Quote Originally Posted by craig View Post
    You need to wrap your latex in MATH codes.

    Is your vector T(t) = (t\cos(t), t\sin(t),0>, not sure what the \sqrt{t^2*cos^2(t)+t^2*sin^2(t)} is?
    Sorry about that.

    \sqrt{t^2*cos^2(t)+t^2*sin^2(t)} is the magnitude of R'(t). Since T(t) = R'(t)/|R'(t)|
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  6. #6
    Super Member craig's Avatar
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    So is it the vector T(t) = (t\cos(t), t\sin(t),0> that you want to differentiate?
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  7. #7
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    Quote Originally Posted by craig View Post
    So is it the vector T(t) = (t\cos(t), t\sin(t),0> that you want to differentiate?
    Nah. I differentiated R(t)= <cos(t)+t*sin(t),sin(t)-t*cos(t),1> into R'(t)=<t*cos(t),t*sin(t),0>

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

    When you do that though you are in indeterminate form. So my question is how would I solve it properly?
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  8. #8
    Super Member craig's Avatar
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    Quote Originally Posted by Sgraveyard View Post
    Nah. I differentiated R(t)= <cos(t)+t*sin(t),sin(t)-t*cos(t),1> into R'(t)=<t*cos(t),t*sin(t),0>

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

    When you do that though you are in indeterminate form. So my question is how would I solve it properly?
    Ahh i do apologise. Do they not give you any limits for the value of \cos{t} or \sin{t} in the question then?
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  9. #9
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    Quote Originally Posted by craig View Post
    Ahh i do apologise. Do they not give you any limits for the value of \cos{t} or \sin{t} in the question then?
    No problem. Nope, they just say determine TNB-Frame at the point (1,0,1) which is t=0
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