 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/7/a/solution

Use the double-angle identity

2 sin x cos x = sin 2 x

f (x) = sin x + sin 2 x + sin 3 x .

In the usual Fourier sine series convention,

b_{1} = b_{2} = b_{3} = 1

, all other

b_{n}

vanish, and all cosine coefficients and the constant coefficient vanish.

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