EMAT 6680 Assignment 10:
Parametric Curves

A parametric curve in the plane is a pair of functions

x=f(t)

y=g(t)

 

where the two continuous functions define ordered pairs (x,y). The two equations are usually called the parametric equations of a curve. The extent of the curve will depend on the range of t and your work with parametric equations should pay close attention the range of t . In many applications, we think of x and y "varying with time t " or the angle of rotation that some line makes from an initial location.

Various graphing technology, such as the TI-81, TI-82, TI-83, TI-85, TI-86, TI-89, TI- 92, Ohio State Grapher, xFunction, Theorist, Graphing Calculator 2.1, and Derive, can be readily used with parametric equations. Try Graphing Calculator 2.1 or xFunction for what is probably the friendliest software.

 

 

EXPLORATIONS

 

1. Graph

x=cos(t)

y=sin(t)

for 0 < or = t < or = 2 pi.

 

 

 

 

Notice that when then the graph is

Notice, when then the graph is

When then the graph is as follows.

 

How would you change the equations to explore other graphs?

 

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