Find the curvature function (x) for y = sin x. Use a computer algebra system to plot (x) for 0 x 2. Prove

Find the curvature function κ(x) for y = sin x. Use a computer algebra system to plot κ(x) for 0 ≤ x ≤ 2π. Prove that the curvature takes its maximum at x = π/2 and 3π/2.  As a shortcut to finding the max, observe that the maximum of the numerator and the minimum of the denominator of κ(x) occur at the same points.