AS/A2 Pure 4 Pure 6

P5 Topic 1: Coordinate Systems
P5.1
Investigate these families of parametric curves, particularly any cusps that may appear.
(a) The epicycloid	x = (a+b)cos t -acos[(a+b)t/a] y = (a+b)sin t -asin[(a+b)t/a] where a and b are arbitary constants
(b) The astroid	x = acos3 t y = asin3 t where a is an arbitary constant
(c) The trochoid	x = at-bsin t y = a - bcos t where a and b are arbitary constants

Summary This problem is adapted from "A-Level Investigations with Omnigraph" Based on free Java applets from JavaMath