The following data represents the average monthly temperatures in Fahrenheit for a city in Alaska. So we're given a bunch of data, and then we're asked to answer the following questions. We're going to use a graphing utility to draw a scatter diagram for the data of one period. So the first thing we're going to do is we're going to grab our graphing calculators. We're going to start a new document, So up here at the home key #1 I'm not going to save any of my old data. And we're going to put in a list and spreadsheet. And this is actually going to look a lot like Excel does. So we're going to put in a list and spreadsheet. If we arrow all the way up, we're going to label the first column as a month. When I come off of that first column, it's going to go from metallics to just regular, and then I'm going to literally put in 1234567891011 and 12:00. And then I'm going to come over to this other column and I'm going to go up to the top and I'm going to type in temp and then I'm going to put in 24.428 point, 833 point 139.9, 47.4. I got to keep looking 53 point, 256.455 point, 449.642 point 432.4 and 27.3. So now we have all the data inputted. We're actually going to insert a new page. So control I is a shortcut for insert, and we're going to insert a data and statistics page, and we're going to have all these points. If I take my arrow down here and click, I can choose which variable I want to be along the X axis. We want months now if I come over to the Yi can click and choose which variable I want for that one and I want temp there in the problem it tells us our window. So we're going to go to menu and we're going to set our window and we want our window settings to be zero to 13 13. I forgot 0. OK, let's go back to the problem. Zero to 13, zero to 60, so zero to 13 and then here zero to 60. So now we get a graph that looks like this. So when we have this current graph, we're going to then go decide which one it looks like in our multiple choice. So coming back here, it's going to look like letter B. If you don't see that, remember that this magnifier means that you can make it way bigger so that you can analyze it based on your graph. So B in this case is going to be our answer. When we look at our calculator at the same time, then it wants us to find by hand a sinusoidal function of the form. So when we're doing this by hand, what we're really doing is we're going to look for the highest value, and the highest value is going to occur at this 56.4. And then we're going to take the lowest value and that's going to be this 24.4 and we're going to divide it by two for the amplitude. And if we do this, we get 16. Then we know that 2π divided by Omega equals our period and this is a full year, so the period is 12. So if we cross multiply, we get 2π equaling 12 Omega or Omega equal 2π twelves, which we are going to reduce to Pi 6. So that's where our Omega came from. Continuing with this problem, it wants us to figure out our fee. Well, we have our high. If we thought about a regular sign graph with a period of 12, here would be 12, here would be 6, here would be 3. But our new high is now at the month 7. So we're going to have 7 -, 3 or 4. So it's shifted 4, but we have to also multiply it by the period, so 4 * π six because it's changing what we're doing. SO4PI6 reduces to 2π thirds and that's where that fee comes from. So the next part wanted us to figure out what the vertical shift would be, and if we did 56.4 + 24.4 and divided by two, we would find that that's 40.4. So now we want to draw in the sinusoidal function found in Part B on the scatter diagram. Going back to our calculator, we're going to go to menu, and we're going to go to analyze, and we're going to plot a function #4 So it gives me F1X. And when I plot this function, I've got to use all that information I had a minute ago, and that information I'm going to have to go back and look at. It is going to be 16 sine Pi 6 - 2π thirds so 16 sine PI6 π / 6 * X - 2π / 3 and then plus that value 40.4. So now we get this nice graph with this line in it. We can grab this function to get it out of the way. If we go to our open hand and click and hold the center key in the middle, it will allow me to drag it around. So the center key right here in the middle. So now when we go back to the problem and we're looking at it, we can see like at the bit at the end, it's a little lower and then it goes through, and then that points above and that points above, and that points above and it goes through and the point here is below and below. So when I look at this, I can see if I magnify them once again, that this looks pretty close to the graph I just had. So then it wants us to use a graphing utility to find the sinusital function of best fit. So if we go back here, I'm going to see if control undo will take that function away. If I do control undo twice, that'll take that function away. Now I'm going to go to menu and I'm going to go analyze. But this time I want to do a regression and a regression is what's the best fit for the information. And we want to do a show sign us idle. So now this is my best fit. Regression once again, I can click and hold to move the function. I don't know where my function just went, but it's OK. So now we can see this. If we go back to our problem, we can see, oh, I do need the equation because I got to type in the data. Let's see if I can do control. There we go, click and hold and drag. Oh, sorry, I don't know what's going on. OK, so it wanted this value here and this value here. So .52 and 2.09. So .52 and 2.09. And then it wants us to determine which one's the best fit. If we make it big, we will see that this one is the best fit. And if you look, those two should be awfully darn similar. So that's this problem in great detail. Hope it helped.