# Frenet apparatus

I need to calculate the Frenet apparatus for the space curve defined by

$$\overrightarrow{r} (t) = \langle t - cos (t), sin(t), t \rangle$$

so for T I did
$$\overrightarrow{r} \prime (t) = \langle 1 + sin(t), cos(t), 1 \rangle$$
then I got |r'(t)| = $$\sqrt{2sin(t) + 3$$
which i'm pretty sure is either wrong or not simplified. Anyone care to look at my problem?

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## Answers and Replies

dextercioby
Science Advisor
Homework Helper
Lose the spaces in the tex tags...$$and the same for the closure. Daniel. krab Science Advisor Sneaksuit said: I need to calculate the Frenet apparatus for the space curve defined by [tex] \overrightarrow{r} (t) = \langle t - \cos (t), \sin(t), t \rangle$$

so for T I did
$$\overrightarrow{r}' (t) = \langle 1 + \sin(t), \cos(t), 1 \rangle$$
then I got $$|r'(t)| = \sqrt{2\sin(t) + 3}$$
which i'm pretty sure is either wrong or not simplified. Anyone care to look at my problem?

hmmm...i can't seem to get Latex to work properly
I fixed the LaTeX, and other problems...

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Thanx for the latex help. Now, do u see a problem with the math?

dextercioby
Science Advisor
Homework Helper
Everything is okay with your exercise.

Daniel.

Ok, but then that gives me
$$T(t) = \frac{(1 + sin(t))i + (cos(t))j + k} {\sqrt{2sin(t) + 3}}$$
Now for T'(t) I don't ever remember taking derivatives of vectors this complicated. Do I use the quotient rule?

dextercioby
Science Advisor
Homework Helper
Okay,that's r' vector which is indeed the tangent vector.Now why would you need another derivative wrt to "t"...?Curvature,torsion...?

Daniel.

Yes, I need the entire Frenet apparatus....tangent, normal, binormal, curvature, and torsion.