It has been quite a while since last time I've used Frenet reference frame. Can anybody tell me what am I missing if I'm missing something? Thank you.
$$\gamma\left(t\right)=\left(t-\sin\left(t\right),\,1-\cos\left(t\right),\,4\sin\left(\frac{t}{2}\right)\right).$$
tangent vector $$\mathbf{T}=\frac{1}{2}\left(1-\cos\left(t\right)\,,\,\sin\left(t\right),\,2\cos\left(\frac{t}{2}\right)\right);$$
normal vector $$\mathbf{N}=\sqrt{\frac{2}{3-\cos\left(t\right)}}\left(\sin\left(t\right),\,\,\cos\left(t\right),\,-\sin\left(\frac{t}{2}\right)\right);$$
binormal vector $$\mathbf{B}=\left(\sin\left(t\right)\sin\left(\frac{t}{2}\right)-2\cos\left(t\right)\cos\left(\frac{t}{2}\right)\,,\,-2\cos\left(\frac{t}{2}\right)\sin\left(t\right)+\sin\left(\frac{t}{2}\right)\left(1-\cos\left(t\right)\right),\,\cos\left(t\right)-\cos^{2}\left(t\right)+\sin^{2}\left(t\right)\right);$$
Is this last expression that it makes me wonder if maybe I did something wrong or forgot to normalize something... the expression should be significantly simpler.