Technologically Embodied
Geometric Functions
Cartesian Graphs and Polar Graphs

▿ Overview

You can use the websketch below to observe similarities and differences in the way that the same trig function is graphed in Cartesian and polar coordinate systems.

▹︎ Compare the Graphs

On the left you can see a Cartesian coordinate system, in which a vertical number line (a translation of the y-axis) moves from left to right along with the motion of x, in the process creating the Cartesian graph.

On the right you can see a polar coordinate system, in which a number line (a rotation of the horizontal axis about the origin) rotates counter-clockwise along with the motion of theta, in the process creating the polar graph.

In both cases, the translating or rotating number line has a point indicating the current value of the dependent variable (corresponding to the value of x or theta). The graph is formed by tracing this dependent-variable point as the number line is translated or rotated to indicate the independent variable.

The Geometer’s Sketchpad software is available here.

▹︎︎ The Fine Print

Requirements:

These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.

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