 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/1/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The angle-subtraction identity gives

3 cos θ + sin θ = 2 cos (θ - π /6)

. Thus

cos (θ - π /6) = 1/ 2

, so

θ - π /6 = \pm π /4 + 2 kπ

. Keeping the two values in the specified interval gives

θ = \frac{5 π}{12}, \frac{23 π}{12} .

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