2.6.2.8 Trigonometric Fourier series

Problem: Expand function \( f(x) \) into the trigonometric Fourier series in cosines. 1) \( f(x)=x^{3} \) in \( [0 ; 1] \), 2) \( f(x)=\sin 2 x \) in \( [0 ; 1] \), 3) \( f(x)=\frac{\pi}{4}-\frac{x}{2} \) in \( [0 ; 1] \).