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The data show the average monthly temperatures for Washington, D.C.

a. Use your graphing utility to draw a scatter plot of the data from $x=1$ through $x=12$ .

b. Use the SINe REGression feature to find the sinusoidal function of the form $y=A \sin (B x+C)+D$ that best fits the data.

c. Use your graphing utility to draw the sinusoidal function of best fit on the scatter plot.

A) See explanation for graph.

B) $y=22.6 \sin (0.5 x-2.0)+57.2$

C) $f(x)$ has a range of $[-3,-1],$ see explanation for graph.

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this item asked you to? Here we go. This side I've asked you had three different questions, and the 1st 1 was to dress at a lot of data. So let's go ahead and do that. We're going to select snapped and it and we're gonna type in the data. So we've got one, two, 34 right? 6789 10 11 and 12. What's the second column? Here? We put in 34.6, 37.5, 47.2. Be 6.5. Okay, so we have input all of the data, and they would like to see a scatter plot. So let's go to second step plot. We're going to turn number one on. So know that on that's okay, let's second quit out of that. Let's go to our window. We can have a minimum of local with a minimum of zero Mets of 13 groups paying a scale of one. Why men we can go with a minimum of 30 is sufficient maximum of 83 feel of one. And then let's take a look at the graph. So this is her scatter plot. You've done that part. Okay, so Now let's let's be wants us to do a sign. Regression. So we go to stepped over the couch and we can go down until we come to sign Regression Town down. There it is. It was, I lost it. Let's go back up. We want the sign. A regression. So we pressed and your own sign. I wouldn't say how many iterations we need, but I guess we'll leave. Three list. One is our input was, too. Is the output period is 12 because it's one through 12. We want to store this regression in Weiss and one. So let's select vars y bars function and one and then let's calculate. I don't see what we get for this. Okay, so here we have an equation. It's been stored in wise one, and you can see if I go back to that previous screen is that you're okay. That's gone. Let's go to the graph. See what we have. So this is something that happens often. Um, let's take a look at the viewing window 1st 1st off, let's take a look at the mode that we're in. Are we in degrees or radiance were in degrees, but see first, I want to see what would happen if we switch Radiance. Let's go back door craft. Let's see if that fix things. There you go. So this was See, this was step See to use the graphing utility to draw the sun you sidle function. Let's go back in capture the equation that we have um, we know we have the eight term is approximately point if you 80.0.6 need term is approximately 0.503 But notice how? Yes, this is exactly in the forum, but your text wanted it, you see permits negative the 0.39 approximately. Actually, I don't like how they have plus negative, but that's fine. So it's not negative. It's just 2.39 or nine, and then your need term is 57.17 So there you have it.