Mathematica Tool 3

This Mathematica notebook is designed for  use with Checkpoint 1 in Section 5.4

Here are the data for average monthly highs and lows.

Months={1,2,3,4,5,6,7,8,9,10,11,12};
Highs={43,47,57,67,74,82,86,84,77,66,58,48};
Lows={26,29,36,44,53,62,67,66,59,47,38,31};

We calculate the mean monthly temperatures.

Means = (((Highs +Lows))/2);

We plot the month high low and average temperatures.

HighData= Partition[Riffle[Months,Highs],2];
LowData=Partition[Riffle[Months,Lows],2];
MeanData=Partition[Riffle[Months,Means],2];

ListPlot[{HighData,LowData,MeanData},PlotStyle->{{Purple,PointSize[0.02]},Gray,Blue},PlotRange->{{0,13},{0,100}}]

Now enter values for A, B,(Subscript[C, 1])and δ ( (Subscript[C, 1])and δ standing in for C and D), and compare the graph of the model function to the data.

A="???";
B="???";
(Subscript[C, 1])="???";
δ="???";

f[t_]:=A+B Sin[(Subscript[C, 1]) (t-δ)]
Show[Plot[f[t],{t,0,12},PlotStyle->Red,PlotRange->{{0,13},{0,100}}],ListPlot[MeanData,PlotStyle->{Blue,PointSize[0.02]},PlotRange->{{0,13},{0,100}}]]