Consider the curve given by the intrinsic equation \(s = c\sin\psi\) for values of \(\psi\) between \(-\frac{1}{2}\pi\) and \(+\frac{1}{2}\pi\), and taking the tangent and normal at the point from which \(s\) is measured as axes of \(x\) and \(y\), respectively, obtain expressions for \(x\) and \(y\) in terms of \(\psi\) as a parameter. With the same axes find the locus of the centre of curvature in terms of the same parameter. Discuss briefly the nature of the two curves if the restriction on the value of the parameter is disregarded.