Chapter 13.3, Problem 48E

Curvature of Plane Parametric Curves The curvature of a plane parametric curve $x=f(t),y=g(t)$ is given by

$\kappa =\frac{|\stackrel{\dot{}}{x}\ddot{y}-\stackrel{\dot{}}{y}\ddot{x}|}{{\left[{\stackrel{\dot{}}{x}}^2+{\stackrel{\dot{}}{y}}^2\right]}^{3/2}}$ where the dots indicate derivatives with respect to $t$ .

48. Find the curvature of the curve $x=a\cos \omega t,y=b\sin \omega t$ .