The smooth curve in is given in parametrised form by the function . Let denote arc length measured along the curve.
(a) Express the tangent in terms of the derivative , and show that .
(b) Find an expression for in terms of derivatives of with respect to , and show that the curvature is given by
[Hint: You may find the identity helpful.]
(c) For the curve
with , find the curvature as a function of .