WriteUp #12
Mathematics with Spreadsheets
By Jaepil Han
3. Use the spreadsheet to graph equations in polar form. Try some of the examples from Assignment 11.
All the investigations followed below are made with MS EXCEL.
To do this, first of all, making rows in the very first column as a theta of my spreadsheet by increasing 0.01 until reaching 6.28. This gives us 628 rows by increasing 0.01 from 0.00 to 6.28, as a 2*π.
Second, putting the equation to calculate the value of r.
Third, since (x, y) = (rcos(θ), rsin(θ)), making two more columns of x and y to convering a polarform to the Cartesian coordinate plane.
Last, making a scatter plot of the last two columns, x and y.
Example 1.
It looks like an ellipse that has a xaxis as its major axis. To verify this conjecture, we need to convert the equation into the Cartesian coordinate form.
Here's the MS Excel file for Example 1.
Example 2.
It looks like another ellipse that has a positivesloped line as its major axis.
Here's the MS Excel file for Example 2.
As an exercise, I do several extensions of the Example 2.
Example 21. The 8 makes the graph smaller. It seems that the numerator of the equation affects the size of the graph. Here's the Excel file for Example 21.

Example 22. When we replace the subtraction by addition, the result graph looks like a reflection of the originial graph by yaxis. Here's the Excel file for Example 22.

Example 23. When we replace the sin by cos, the result graph looks like a reflection of the originial graph by xaxis. Here's the Excel file for Example 23.

Example 24. When we replace the sin by cos and the subtraction by addition, the result graph looks like a reflection of the originial graph by xaxis. Here's the Excel file for Example 24.
