Lesson 23

Part III (Introduction to 3D Graphing, continued)

In this part, we will work with parametric equations. In 2-dimensional space, we have one parameter, t, to map two variables onto a curve. In 3-dimensional space, we have two parameters, s and t, to map three variables onto a surface. The ClassPad makes exploring parametric equations in 2- and 3-dimensions fun and somewhat easy to understand!

1. Exploring the parametric form of a circle in 2-dimensions

2. Exploring the parametric form of a sphere in 3-dimensions

Part III


Practice Exercises

  1. Open the 3D-Graph application and clearing the editor, if needed.
  2. Graph the parametric equation shown below:
  3. Resize the window so that only the graph shows.
  4. Rotate the graph until you like the way it looks.
  5. With the graph showing, get a screen capture. Paste it into your Lesson23 document (under a title of PART III).
  6. Modify your parametric equation by changing the 2’s to 1’s:
  7. Graph again and resize the window so that only the graph shows.
  8. Rotate the graph until you like the way it looks.
  9. With the graph showing, get a screen capture. Add two blank spaces following the first screen capture and then paste this one.
  10. Yes, this is an easy lesson! But, you deserve to relax and begin your vacation early. Thank you for completing the course.

Part IV

Written Exercises

Please copy and paste the following questions into your Lesson23 document (under a title of Part IV) and answer them.

  1. What will z=-x+5y+1 look like when graphed?
  2. How can we display two graphs at one time?
  3. What does the z=cos(x) look like graphed?
  4. If you were to plot (0,4,3), describe where it would be.

Reflection Exercises

You have just completed the twenty-third lesson in ClassPad 101. The end! Thank you for completing ClassPad 101 and all your suggestions. Please take a few moments to copy and paste the following four questions at the end of your Lesson23 document and answer them.

  1. Approximately how long did it take you to complete this lesson?
  2. Is there any area or areas that you think we should have spent more time on?
  3. Do you think that you will be comfortable using the ClassPad in your future math classes?
  4. Would you recommend this class to others? If so, why? If not, why not?

Assessment 23: Introduction to 3D Graphing