MATLAB: How to do “Cosine wave approximation“ for random plot data

Question

I want to do "Cosine wave approximation“ for randam plot data.

Is there a way to forcefully approximate the following data?

Also please tell me about how to do it．

x = [0.087266463 0.261799388 0.436332313 0.610865238 0.785398163 0.959931089 1.134464014 1.308996939 1.483529864];

y = [22 22 16 13 13 9 3 0 3];

Answer 1

easy peasy. Though I have no clue what it means to "forcef\ully approximate".

x0 = [mean(y),max(y) - min(y)/2,0,3];
ft = fittype('a + b*cos((x-c)*d)')
ft = 
     General model:
     ft(a,b,c,d,x) = a + b*cos((x-c)*d)
mdl = fit(x',y',ft,'startpoint',x0)
mdl = 
     General model:
     mdl(x) = a + b*cos((x-c)*d)
     Coefficients (with 95% confidence bounds):
       a =       11.96  (7.416, 16.51)
       b =       10.43  (4.97, 15.88)
       c =    -0.02594  (-0.8867, 0.8348)
       d =       2.079  (0.141, 4.017)
plot(x,y,'o'),hold on,plot(mdl)