The set S = " 1 2 , cos x, cos 2x, cos 3x, cos 4x ( is an orthonormal set of vectors in
Chapter 5, Problem 9(choose chapter or problem)
The set S = " 1 2 , cos x, cos 2x, cos 3x, cos 4x ( is an orthonormal set of vectors in C[, ] 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: (a) ! sin4 x cos x dx (b) ! sin4 x cos 2x dx (c) ! sin4 x cos 3x dx (d) ! sin4 x cos 4x dx
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