 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/15e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

p_{0} = \frac{1 + Re e ^{2 πi θ}}{2} = \frac{1 + c o s ( 2 π θ )}{2} = cos^{2} (π θ) .

Thus

cos (2 π θ) = 2 p_{0} - 1,

θ = \pm (2 π)^{- 1} arccos (2 p_{0} - 1) (mod 1)

. This test alone cannot distinguish

θ

from

1 - θ

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