How to Graph Cardioids on a Calculator

Cardioids are best rendered when using polar coordinates.

A cardioid is the curve described on a plane by a point on a circle, as that circle makes a complete turn rolling around another circle with a single point of contact between the two. When plotted on a set of Cartesian x-y coordinates, the cardioid resembles a stylized representation of a heart. Because there's an infinite number of values of x for which the cardioid has more than one value of y, it can take two y=f(x) curves plus careful range settings to graph cardioids on a calculator. However, many common graphing calculators can graph a cardioid much more elegantly using polar coordinates.

Instructions

1. Configure the calculator so that it draws function graphs using polar coordinates. For example, on a TI-85, bring up the Mode page by pressing [2nd],[MORE]. Using the arrows, scroll to the line reading "Func Pol Param DifEq" and highlight "Pol;" press [ENTER].

2. Enter graphics mode. On the TI-85, press [GRAPH].

3. Enter the equation for a sample cardioid in polar coordinates, say

   r(theta) = 1-sin(theta)

   By default, theta will range between 0 and 2 x Pi, so there is no need to set that. On the TI-85, type [F1][1][-][SIN][F1]

   for the sample cardioid. Press [ENTER].

4. Graph the function. On the TI-85, press [F5]. The cardiod will display on the calculator screen.

References

• University of Georgia: Polar Equations