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


Download the original Sketchpad file.      Download the student worksheet.      Download the teacher notes.     

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.

This activity is adapted for Web Sketchpad from the activity book Exploring Precalculus with The Geometer’s Sketchpad, published by McGraw-Hill Education.

The Geometer’s Sketchpad software is available here.

▹︎︎ The Fine Print


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.

Release Information

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Update History:

07 Apr 2017: Created this page.