2.6.2.15 Trigonometric Fourier series

Problem: a) Expand function \( y=f(x) \), given on the halfcycle \( (0 ; l) \), into Fourier series in cosines. Plot the graphs of the 2nd and 3rd partial sums. Write Parseval's equality for the resulting series. b) Expand function \( y=f(x) \), given on the halfcycle \( (0 ; l) \), into Fourier series in cosines. Plot the graphs of the 2nd and 3rd partial sums. c) Expand function \( y=f(x) \) into Fourier series, continuing it on the half-cycle \( (0 ; l) \) with a function, equal to zero. Construct the graphs of the second and the fourth partial sums. \[ y=1-x, \quad l=4 \]