Polar Graphing

After writing yesterday’s post on the connections between polar and Cartesian graphs, I realized that I hadn’t said anything about how easy it is to start from scratch and create a polar graph in Sketchpad, so I decided to write this post, and include an instructional video. Here are the steps to create the graph shown on the right below.

Simple Polar Graph

  1. Choose Graph | Plot New Function.
  2. Use the Equation menu to choose r = f(θ).
  3. Type “c” (for “cos”), “2″, and “th” (for “theta”).
  4. Click OK.
  5. If your angle units are degrees, Sketchpad may ask if you want to change to radians. (Don’t worry; the graph will be correct no matter whether you want to use radians or degrees.)

That’s it!

This short video shows how easy it is to add parameters to control the amplitude, period, and phase shift:

It’s also easy to create a family of polar functions. Once you’ve modified your graph to show f(θ) = a·sin(b·(θc)), here are the steps used to graph the family of functions shown below.

Family of Polar Graphs

  1. Select both the graph and parameter a.
  2. Choose Construct | Family of Functions.
  3. Set the domain to go from 1 to 6, and the number of samples to 11. This will create samples for these values of a: {1.0, 1.5, 2.0, …, 6.0}.
  4. Click OK.

You’re done. Now experiment on your own!


About Scott Steketee

Scott Steketee taught secondary math and computer science in Philadelphia for 18 years and received the district's Teacher of Excellence award. Since 1992 he has worked on Sketchpad software, curriculum, and professional development for Key Curriculum Press and KCP Technologies. He also teaches Secondary Math Methods in the graduate teacher education program at the University of Pennsylvania.
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5 Responses to Polar Graphing

  1. Pingback: Cartesian and Polar Graphs |

  2. avatar Nguyen Nguyen says:

    I love it!!! I was just reading an article published in Mathematics Teachers on Graphing Polar Curves by Jonathon Lawes (May 2013 Issue). This goes perfectly well with that article. Thanks for sharing

  3. Hello There. I found your blog using msn. This is a very well written article.

    I’ll make sure to bookmark it and return to read more of your useful info. Thanks for the post. I will definitely comeback.

  4. avatar Suzy Yoon says:

    Hi Scott! Do you remember me from Penn GSE?
    I wanted to purchase the book “exploring statistics with fathom” but cannot find any information on purchasing anywhere on the KCP website.
    Could you direct me?

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