How to find unknown parameters in a nonlinear least squares function?

I have the rest of the code already complete, however, I believe I have the c1 and c2 unknown paratmers wrong and I am not sure how to solve for them. How would I enter the correct values of c1 and c2 considering the equation given above?

clc

close

load Downloads/dataSet1.mat t f;

subplot(4,1,1);

leastSquares(t,f,1);

load Downloads/dataSet2.mat t f;

subplot(4,1,2);

leastSquares(t,f,2);

load Downloads/dataSet3.mat t f;

subplot(4,1,3);

leastSquares(t,f,3);

load Downloads/dataSet4.mat t f;

subplot(4,1,4);

leastSquares(t,f,4);

function leastSquares(t, f, dataNum)

plot(t, f, '*r', 'MarkerSize', 3)

xlabel('x')

ylabel('y')

title(['Nonlinear Fit of Experimental Data Set #' num2str(dataNum)])

grid minor

hold on

t = t(:);

f = f(:);

A = [(t.^0.8)./(cos(3*t).^2),t.^0.8];

B = 1./f;

X = inv(A'*A)*A'*B;

c1 = X(1);

c2 = X(2);

tF = min(t):0.001:max(t);

fF = (tF.^0.8)./(c1*cos(3*tF).^2 + (1/c2));

plot(tF, fF, '-k')

legend('Experimental Data Points','Least Squares Fitted Curve', 'Location', 'best')

hold on

fH = (t.^0.8)./(c1*cos(3*t).^2 + 1/c2);

fB = mean(f);

R2=abs(1-sum((f-fH).^2)/sum((f-fB).^2));

fprintf('The results for Data Set #%d\n',dataNum)

fprintf('c1 = %.4f\n', c1)

fprintf('c2 = %.4f\n', c2)

fprintf('R^2 = %.4f\n\n', R2)

end

[Leonardo Guzman]

If needed these are the data sets used in the program.

Answer 1

[Torsten]

A = [cos(3*t).^2,ones(numel(t),1),];
B = t.^0.8./f;
X = A\B;
%or X = inv(A'*A)*A'*B;
c1 = X(1);
c2 = 1/X(2);

instead of

A = [(t.^0.8)./(cos(3*t).^2),t.^0.8];
B = 1./f;
X = inv(A'*A)*A'*B;
c1 = X(1);
c2 = X(2);