A pair of functions f and g are said to be orthogonal on the interval [a, b] if b f (x g (x dx a = 0. a family of functions is said to be orthogonal on [a, b] if each distinct pair of functions f? g in the family is orthogonal on [a, b]. in this problem, you will show that the family of trigonometric functions sin (x, cos (x, sin (2x, cos (2x, ..., sin (nx, cos (nx, ... is orthogonal on the interval [0, 2?].
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