Assignment 12

by Rives Poe

In this exploration we are going to use a spreadsheet to do some of the "dirty work" in solving parametric equations. Spreadsheets are a very useful tool in mathematics. They can help us balance our checkbooks, graph productivity in a work place, and solve complex mathematical problems. In this assignment, I will use Microsoft Excel to display the graph of parametric equations.

For the first problem, I will use the equations:

x=(1-t^2)/(1+t^2)

y=2t/(1+t^2)

I must start by entering a value for t in column A1. My initial value for t is 1, then in A2, I typed in 2. To save me time, in cell A3, I typed in the formula =A1+A2, making the value of t in cell A3=3. Then I just filled down and now have 10 values for t.

Next step is to type in the formula for the x coordinate: x=(1-t^2)/(1+t^2). However, I had to change a few things in this formula. The computer doesn't recognize t, so I actually typed in: =(1-A1^2)/(1+A1^2). The spreadsheet recognized this formula and immediately produced the number 0. Next, I highlighted cells B1-B10 and filled down, and TADA the values of the x-coordinates appeared. Now I need to type in a formula for the y-coordinate: y=2t/(1+t^2). Again, the computer does not recognize t, so I used A1 instead, and then filled down to get all the y-coordinate values.

Then, I used the chart wizard to graph my x and y coordinates.

As you can see in the graph above, the blue diamonds are the x and y coordinates at the different values of t.

In the next investigation using spreadsheets we will use the spreadsheet to graph a different equation in parametric form using the equations:

x=t+1

y=2t+1

So, I will begin as I did before, first producing the values for t. This time, I am going to start with t=-3. I will continue in the same fashion as I did for the last parametric equation, using the spread sheet to do the work of solving the equations for x and y. To see the finished product and the graph, click here.

Using a spreadsheet is very helpful. It can organize information quickly and effectively, it can solve equations in a matter of seconds. A spreadheet is a tool that can be used for everyday things such as keeping track of your expenses to solving difficult mathematical problems. In all cases with a spreadsheet a graph can be used to help evaluate what is happening or how things are changing (such as the profits of a new business). I think that students should be exposed to spreadsheets and their uses early on, so that when they are faced with problems that seem to complicated to be done by hand, they will feel comfortable using a spreadsheet to help them solve the problem and come up with different solution strategies.