S = {{4,-8},{7,5},{1/2, 2}, {12,5},{25, 1/4}};

PlotS = ListPlot[S,PlotMarkers->Style["●", 12, Red], Axes->True, AxesOrigin->{0,0}]

S//MatrixForm

(A=Join[Drop[S,{},{2}],Table[{1},{i,1,5}],2])//MatrixForm

B = Drop[S,{},{1}];

B//MatrixForm

PsIA = Inverse[Transpose[A].A].Transpose[A];

PsIA//MatrixForm

(MBsoln = PsIA.B)//MatrixForm

LineApprox = Plot[(1161/14552)*x+(2215/29104),{x,-1,26}];

Show[PlotS,LineApprox]

Plot[Sin[2*π/24*(x-1)],{x,1,25}, AxesOrigin->{0,0}]

Sin[2*π/24*(x-1)]

Sin[2*π/24*(x-1)],Cos[2*π/8*(x+1)],1

a*Sin[2*π/24*(x-1)] + b*Cos[2*π/8*(x+1)]+c

Table[{Sin[2*π/24*(S[[i,1]]-1)],Cos[2*π/8*(S[[i,1]]+1)],1},{i,1,5}]