### Trigonometry T1-84 (Activity)

his activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84.

## Step 1: Get a TI-84 Graphing Calculator (or similar).

• Don’t have one? If you use Windows, you can download the attached Emulator (ZIP file), extract the Zip folder, and run the Wabbitemu.exe file. Load the rom file when prompted and just choose the View > Enable skin option to work with your virtual calculator.

## Step 2: Get some data.

• Go to the Randomized Wave Data Generator and use the form to get some randomly-generated data (check the boxes for more interesting data).
• Your data should be different from every other data set on earth, so copy and paste it to a (spreadsheet or word-processor) file for your later use.

## Step 3: Enter the Data into your Calculator.

1. Press Y= and clear the Y1 function.
2. Press STATPLOT (2nd followed by Y=) and choose Plot1.
3. Under Plot1, select On (press ENTER), after Type select the drawing of disconnected dots, and make sure you have Xlist: L1(2nd followed by 1) and Ylist: L2 (2nd followed by 2).
4. Press STAT. With EDIT highlighted, select 1:Edit…
5. In the table that appears, under L1 type the x values and under L2 type the values of y. Make sure your L1 and L2 lists have the same length.
6. Press ZOOM and choose option 9:ZoomStat to look at a scatter plot of your data.

## Step 4: Find the Sine Wave of Best Fit for the Data.

1. Press STAT. Press the right arrow key to highlight CALC. Then scroll down to select C:SinReg and pressENTER ONCE.
2. [Older Versions] After the word SinReg, which should now be on the screen, enter L1(2nd followed by 1), then type a comma (just above the 7 key), then enter L2 (2nd followed by 2), then type another comma, and then enter Y1 (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1) . Your screen should now read SinReg L1, L2, Y1. Then press ENTER ONCE.
3. [Newer Versions] In the SinReg screen, choose Iterations:3 Xlist:L1, Ylist:L2 and Store RegEq: Y1 (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1). Then highlight Calculate and press ENTER ONCE.
4. The calculator should now display the values for abc, and d in the function f(x)=asin(bx+c)+dthat best fits the given data set.
5. Press GRAPH to see the sine regression function plotted along with your scatter plot and press Y1 to see the equation of your wave.