Vector-valued function: R = sin(t)i + rt cos(t)j + sin(t)k

[whizvish]

So this is just some sample problems our teacher gave us to study from, and I am trying to figure out one of the problems, and did not even know where to begin.

"Consider the curve R = Sin t i + rt(2) cos t j + sin t k,
0 equal to or less than t equal to or less than pi/2"

A. Determine T(0), T(pi/2), N(0), N(pi/2)
== For this part, I figured that you just substitute the T values given into the curve given, but I am not sure for the N values.

B. Eliminate t to determine the cartesian equation of R(t), Put limits on the variables. Verbally describe this curve.
== Does this just mean you take out the t's in the curve given? And then put limits on X?

D. What is the Curvature K at t=0 and t=pi/2
== I'm thinking that I would use the formula |a x v|/v^3 = K and find the curvature at those given values.

Any Help would be greatly appreciated.
Sorry if the things werent easy to understand, It was hard to type up the things, and I had to leave out the vector symbols.

Thanks =)

 

[stapel]

The variable "t" and the function "T" are not the same thing.

Have you perhaps missed a lot of class sessions...? Because this exercise is asking you for curvatures (\(\displaystyle \kappa\)), normals (N), tangents (T), and torsions (\(\displaystyle \tau\)), but you appear to be unfamiliar with any of these notations or concepts...?

Eliz.

 

[pka]

Re: Vector-valued function: R = sin(t)i + rt cos(t)j + sin(t

"Consider the curve R = Sin t i + rt(2) cos t j + sin t k,
0 equal to or less than t equal to or less than pi/2"
A. Determine T(0), T(pi/2), N(0), N(pi/2)
== For this part, I figured that you just substitute the T values given into the curve given, but I am not sure for the N values.

It seems that you have a good bit of confusion as to what T & N are.
\(\displaystyle T = \frac{{R'}}{{\left\| {R'} \right\|}}\) this is known as unit tangent.

The unit normal is \(\displaystyle N = \frac{{T'}}{{\left\| {T'} \right\|}} = \frac{{R' \times \left( {R'' \times R'} \right)}}{{\left\| {R' \times \left( {R'' \times R'} \right)} \right\|}}\).

In other words T & N are vector functions based on R’ & R”.

 

[whizvish]

Wow big error on my part, and we just covered that part yesterday. >.>
but yeah. so A is alright then since I would just have to take the derivative of R
What about the rest?
Thanks for the quick replies.