 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/9/solution

The original PDF contains the product

sin x (1 + 4 cos x)

; the transcription drops the

x

after the first sine. Using

2 sin x cos x = sin 2 x

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

Thus

b_{1} = 1

b_{2} = 2

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