National Aeronautics and Space Administration Glenn Research Center Learning Technologies Project

# SINE AND COSINE GRAPHING

Question: What is the relationship between a Cosine and Sine curve?

This exercise is designed to integrate the use of Appleworks in a mathematics classroom. Although the instructions are for Appleworks, sample data is given and can imported into any spreadsheet program. The purpose is to show how spreadsheet programs can be easily implemented into a classroom setting. A Appleworks version of the instructions are available to be downloaded and used off-line.

### HOW TO CREATE A GRAPH OF A SINE WAVE AND A COSINE WAVE USING Appleworks SPREADSHEETS

1.
2. Double Click on the Appleworks Icon.

3. Click on the circle for a new spreadsheet.

4. Put the cursor in cell "A1" and click to highlight.

5. Type the word "Degrees".

6. Press Tab and type "Radians". Press Tab again and type "Sine", press Tab and type "Cosine".

7. Move the cursor to cell A2, click to highlight. Type in the following degrees into column A starting with cell A2:
```		0		120		210		300
30		135		225		315
45		150		240		330
60		180		270		360
90
```

8. Highlight cell B2. Click on Edit and drag to Paste Function. Within the pop up menu, scroll to the function called Radians(degree number). Double click on this function. You will notice in the text box, "degree number" is highlighted in blue. You need to put a number representing degrees in place of those words. Since in column A you have the list of degrees you want to manipulate, you can just click on cell A2. Now you will notice that A2 appears where the words degree number use to be. Press return. What has happened is the radian of 0 degrees has been calculated and the result is now listed in cell B2.

9. Now click on cell B2 and hold and drag to cell B18, so that all of the cells in-between are highlighted. Click on Calculate and drag to Fill Down. You will now notice that the radians of all of the degrees listed in column A have now been calculated.

10. You will notice that the format of the numbers that have been calculated are in scientific format. To make the numbers easier to read, keep the same set of cells highlighted, B2 through B18. Click on Format and drag to Numbers. In the pop up menu, click in the circle in front of the word fixed. In the blue box, next to the word precision, type a "3". Click OK. Notice now that your radians are all displayed in decimal format to the thousandth place.

11. Highlight cell C2. Click on Edit and drag to "Paste Function." Now scroll to the function Sin(number). Click on Sin(number) and click on OK. Again notice in the text box that the word "number" is highlighted. Just as we did for the radians, click on cell B2 and press return. The sine of 0 radians has just been calculated.

12. Highlight cells C2 through C18, click on Calculate and drag to Fill Down to calculate the sine of all of the radians listed in column "B."

13. Just as we did before, click on Format and drag to Numbers. In the pop up menu, click in the circle in front of the word "fixed." In the blue box, next to the word precision, type a "3". Click OK.

14. Now do the next column on your own. Find the Cosine of the radians listed in column B.

15. Now we will graph Degrees vs. the Sine and Cosine of those degrees. To graph all of the columns that are going to be graphed have to be next to each other so we need to move the degrees column next to the sine column.

16. Click on the letter C in the column headings to highlight the entire C column. Click on Calculate and drag to Insert Cells.

17. Now highlight cells A1 through A18. Click on Edit drag to Copy. Now highlight cells C1 through C18, click on Edit and drag to Paste.

18. Now we are ready to graph. Click on cell C2 and drag to cell E18. Click on Options and drag to Make Chart.

19. We will go through each of these options listed on the left hand side starting with "Gallery" which is currently active.

20. "Gallery" is where the type of chart is chosen. Click on the box with the word "Line" underneath it.

21. Next click on "Axis." Notice that the Y axis circle is darkened, we will first be working with this axis. In the box next to the words "Axis label" type "Sine/Cosine". If you would like to change where the tick marks are located, you may use the pull down menu next to the words "Tick Marks". Additionally, when the box next to the words "Grid Lines" has an "X" in it, grid lines will be displayed on your graph when the box is empty, there will not be grid lines. Now click in the circle next to the words "X axis". In the box next to the words "Axis label" type "Degrees". Again, choose where you would like the tick marks and whether or not you want grid lines.

22. Click on "Series." This pop up menu will let you specify what your data points will look like. You can choose whether or not you want your data points labeled and where around the data point you want it displayed. Make sure the box next to "Label Data" has an "X" in it and click in the center left hand circle below it. In the pull down menu next to the words "Edit Series," choose "Series 1." Make sure the box next to the word "Symbol" has an "X" in it and click on the hexagon symbol. Next choose "Series 2" from the pull down menu next to the words "Edit Series", make sure the box next to the word "Symbol" has an "X" in it and click on the diamond symbol.

23. Click on "Labels" Type in the text box next to the word "Title" "Sine Wave and Cosine Wave Plot" Click on the box next to the word "Legend" so there is no "X" in that box.

24. Click on "General" In the lower right hand column where the words "Use numbers as labels in 1st row and 1st column" appear, click on the box next to "1st Column" Click "OK"

25. With the pointer click and hold on the chart you have just made and drag it to the upper left hand corner of your screen. Now place the pointer on the lower right hand black square, click and hold and drag towards the lower right hand corner of the screen to make the chart larger.

Current view of chart

26. If there are any further modifications to be made to the chart, highlight the axis or the title, for example, and use the format menu to change the font, size, style, etc. of the text. Also click on "Options" and drag to "Modify Chart" to go back to the pop up menus that were just used to make the chart.