Curvature function for the graph of cosine
The locus of the given regular parametric curve is the graph of the cosine function over [0,2\pi]. Below is the graph of the curvature as a function of the parameter t, which agrees with x in this parametrization. Clicking play, observe the motion of X and the evolution of the moving frame {T,U} along the curve, where T is the unit tangent vector and U is the unit normal vector. The curvature function is positive where T is turning toward the unit normal and negative where it is turning away from the normal.