Question

Find the vectors T, N, and B at the given point.
r(t) = <9 cos t, 9 sin t, 9 ln cos t>, (9, 0, 0).

Answer 1

$$\vec{r}'(t)=(-9\sin t,9\cos t,-9\tan t)=9(-\sin t,\cos t,-\tan t)$$normalize to find \(\vec{T}\). then find its derivative and normalize to determine \(\vec{N}\). repeat on \(\vec{N}\) for \(\vec{B}\)

Answer 2

When I normalized I got \[\sqrt{82+\tan ^{2}x}\] but I am not sure if that is correct. Could you double check me on that?