Given a function F which consists of X and Y parametric equations,
each expressed as a function of the same independent variable t.In general it is difficult for the students to imagine the graph of F.Using the Applet of Parametric Equations, the graph of F can display and the visual
explanation for the table of the derivatives of X and Y can be given. |

In this applet you can find the locus of F, dragging the point A.The button of@" Init"@is for replacing the figure in the initial state.The button of@" Clear"@is for clearing the locus of F.In the picture on the lower left, the ratios of p and q to 1 are displayed.Where p and q are the circular frequency of X and Y respectively.If you drag the yellow and green points, p and q will be changed respectively.In the picture on the right, if you drag the yellow and green circles, the radii of rx and ry will be changed respectively. |

Given parametric equations |

To imagine the funation F, a table of derivatives of X and Y is often used.What is the reason we use it? The table of the derivatives of X and Y is illustlated below. |

Using this applet, you can see movements of X and Y.
Now take notice of
That is true of
Therefore if you know the derivatives of |