# Introduction to parametric curves

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).

**With the ‘Show/hide parametric curve’ box unchecked and t fixed.**What will you notice about A’s movements? What about B’s movements? Will A and B ever have the same value ?

**With the box unchecked and the slider bar animated.**Work out the coordinates of some points the curve will pass through. What symmetry are you expecting to see?

**With the box checked and the slider bar animated**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? Try other parametric equations with the appropriate range for t

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