I'm learning differential geometry, specifically the theory of curves, and need help with the following exercise:
Consider the curve $\boldsymbol\alpha(s)$ of $E^3$ with (unit) normal vector given by
$$\mathbf N(s) = (\sin(s), 0, \cos(s)).$$
$(a)$ Show that $\boldsymbol\alpha(s)$ has constant curvature and constant torsion.
$(b)$ Identify the type of the curve.
If we assume that $(a)$ is true, i.e. if both curvature and torsion are constant, then $\boldsymbol\alpha(s)$ is a circular helix. This result is mentioned in my textbook by means of an example (without rigorous explanation).
I still need to prove $(a)$ but I don't know how to do so. Since we are not given the parametrization of $\boldsymbol\alpha(s)$ explicitly, we can't compute the well-known formulas for curvature and torsion. I thought I could use the Frenet formulas but I could not come up with something useful.