# Frenet apparatus

1. Feb 7, 2005

### Sneaksuit

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?

Last edited: Feb 7, 2005
2. Feb 7, 2005

Lose the spaces in the tex tags...$$and the same for the closure. Daniel. 3. Feb 7, 2005 ### krab I fixed the LaTeX, and other problems... Last edited: Feb 7, 2005 4. Feb 7, 2005 ### Sneaksuit Thanx for the latex help. Now, do u see a problem with the math? 5. Feb 7, 2005 ### dextercioby Everything is okay with your exercise. Daniel. 6. Feb 8, 2005 ### Sneaksuit Ok, but then that gives me [tex] T(t) = \frac{(1 + sin(t))i + (cos(t))j + k} {\sqrt{2sin(t) + 3}}$$
Now for T'(t) I don't ever remember taking derivatives of vectors this complicated. Do I use the quotient rule?

7. Feb 8, 2005

### dextercioby

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

Daniel.

8. Feb 8, 2005

### Sneaksuit

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