To solve this problem, we follow the following steps:
1) First, we organize our set of measurements. We separate them into x and y values.
The x-values would be: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
The y-values would be: 2.29, 1.89, 1.09, 0.23, -0.80, -1.56, -2.18, -2.45, -2.29, -1.75, -1.01.
2) Next, we construct two matrices, matrix A and matrix B, based on these x and y values.
For matrix A, we model it based on the polynomial function f(x) = c₁sin(0.4x) + c₂cos(0.4x). So, each row in matrix A would be a pair of values [sin(0.4x), cos(0.4x)] for each x-value.
Matrix B would simply be the array of y-values.
3) After that, we solve for the least squares solution of the equation Ax = B. This implies calculating the values of c₁ and c₂ that minimize the square of the difference between the left and right sides of the equation, over all examples.
The least squares solution returns the coefficients of the polynomial, which are -0.691836754049027 (c₁) and 2.320723856788306 (c₂).
4) So, the polynomial that best fits our measurements, based on the least squares approach, is f(x) = -0.691836754049027sin(0.4x) + 2.320723856788306cos(0.4x).
5) Regarding the constant term co from the polynomial f(x) = cos(0.4x), it represents the y-intercept of the function. Comparing it to the resulting polynomial, it seems that our function is not merely a standard cosine function with a y-intercept, but a complex wave pattern combined with sine and cosine functions. This indicates the complexity of the data we are trying to model, as it is not straightforward enough to be modeled by a simple linear or cosine function.