How to Graph Cardioids on a Calculator

Written by jonah quant
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How to Graph Cardioids on a Calculator
Cardioids are best rendered when using polar coordinates. (graph image by Roman Sigaev from

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 stylised 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.

Skill level:


  1. 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. 2

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

  3. 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. 4

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

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