ClearAll; hour = Table[i - 1,{i,76}];
period = 621/25;
factor = 200/207;
tide = {3.9, 3.4, 3.0, 2.8, 3.0, 
         3.6, 4.4, 5.1, 5.7, 6.0, 
         5.6, 4.8, 3.9, 3.4, 2.6, 
         1.9, 1.2, 1.0, 1.3, 2.3, 
         3.2, 4.0, 4.3, 4.5, 4.2, 3.8, 3.3, 3.0, 2.8, 
         3.1, 3.6, 4.5, 5.3, 6.0, 
         6.2, 5.8, 5.1, 4.3, 3.4, 
         2.6, 2.0, 1.6, 1.6, 2.2, 
         3.1, 3.9, 4.5, 4.7, 4.6, 4.2, 3.5, 3.0, 2.6, 
         2.5, 2.8, 3.5, 4.3, 4.9, 
         5.4, 5.5, 5.1, 4.4, 3.5, 
         2.8, 2.2, 1.7, 1.5, 1.8, 
         2.6, 3.4, 4.1, 4.5, 4.5, 4.2, 3.7, 3.1};
data = Map[Thread,Transpose[{hour,tide}]];
circl = Graphics[Disk[{36-period,g[36+period]},{0.5,0.075}]];
circm = Graphics[Disk[{36,g[36]},{0.5,0.075}]];
circr = Graphics[Disk[{36+period,g[36+period]},{0.5,0.075}]];

g[t_] = Fit[data,{1,Cos[factor Pi t/12], Sin[factor Pi t/12],
					 Cos[factor Pi t/6],  Sin[factor Pi t/6]},t];
bestfit = Plot[g[t],{t,0,75},PlotPoints->100,
				Ticks->{{{36-period,"t-p"},{36,"t"},{36+period,"t+p"}},{{g[36],"f(t)"}}},
				PlotRange->{{0,75},{0.5,6.5}},
				AxesOrigin->{-2,0.4},
				PlotLabel->"Figure 23.2"];
Show[bestfit,circl,circm,circr,Ticks->{{{36-period,"t-p"},{36,"t"},{36+period,"t+p"}},{{g[36],"f(t)"}}},
				PlotRange->{{0,75},{0.5,6.5}},
				AxesOrigin->{-2,0.4},
				PlotLabel->"Figure 23.2"]