# Fitting results on two part graph

I have to do fitting of some experimental data that in the end should be represented like this:

For the left part of graph from $$(\pi,0)$$ to $$(0,0)$$ experimental data is given as:

data_left={{0.20,28.26},{0.40,66.15},{0.45,62.80},{0.7,107.4},{0.92,145.2},{1.00,143.8},{1.3,172.74},{1.56,184.15},{1.9,178.52}};


and the data for the remaining part of plot is:

data_right={{0.3,27.10},{0.61,57.01},{0.54,66.51},{0.77,87.9},{0.83,90.74},{1.1,117.81},{1.57,166.30},{2.52,198.10},{3.15,216.63},{4.72,166.30}};


I would like to find graph which is represented with black line as a result of a fitting with model:

model[x_,y_]:20*Sqrt[(a-b+Cos[y])^2-(Cos[x](Cos[y]+a))^2]


and to find parameters $$a$$ and $$b$$ that fit data on both parts. Is there some way in which I can do this in Mathematica?

• Your data is 2D but your model is 3D? – Okkes Dulgerci Feb 7 at 16:19
• Model function would take values for (x,y) in two parts: from (\pi,0) to (0,0) and from (0,0) to (0,2\pi) and give some value so it can be in general plotted in such a way, because one variable is 0 when other is changed. – Theorist Feb 7 at 16:27
• So does x go from Pi to 0 with y = 0 and y go from 0 to 2 Pi with x = 0? Really not very clear. If we change the sign of the x values for the data_left are we getting your plot on a continuous axis going from -Pi to 2 Pi? – Hugh Feb 7 at 16:49
• For data_left I have y=0, and x is varied from 0 to Pi, and for data_right, x is 0 and the y values are in interval from 0 to 2*Pi. – Theorist Feb 7 at 16:53
• I have previously asked question about these plots. See post mathematica.stackexchange.com/questions/182723/…. Now I am interested is there a way of performing fit with some data with model given. – Theorist Feb 7 at 16:57