The set is an orthonormal set of vectors in C[-Ï, Ï] with inner product defined by (2).

Question:

The set

is an orthonormal set of vectors in C[-Ï€, Ï€] with inner product defined by (2).
(a) Use trigonometric identities to write the function sin4 x as a linear combination of elements of S.
(b) Use part (a) and Theorem 5.5.2 to find the values of the following integrals:
(i) ˆ«Ï€-Ï€ sin4 x cos x dx
(ii) ˆ«Ï€-Ï€ sin4 x cos 2x dx
(iii) ˆ«Ï€-Ï€ sin x cos 3x dx
(iv) ˆ«Ï€-Ï€ sin4 x cos 4x dx