This applet is designed to help students build on their understanding of the behaviour of functions f(x) and g(x) to appreciate the features of the curve with parametric equations x=f(t), y=g(t).

[b]With the ‘Show/hide parametric curve’ box unchecked and t fixed.[/b][br]What will you notice about A’s movements? What about B’s movements? Will A and B ever have the same value ?[br][br][b]With the box unchecked and the slider bar animated.[/b][br]Work out the coordinates of some points the curve will pass through. What symmetry are you expecting to see?[br][br][b]With the box checked and the slider bar animated [/b][br]Substitute for x and y in the identity sin^2(t)+cos^2(t)=1. What is the Cartesian equation? At what value(s) of t does the ellipse cross the line y=x? What difference would you notice if you had used x(t)=4cos2t and y(t)=2sin2t? [br][br]Try other parametric equations with the appropriate range for t