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Home » So $ f $ is both additive and multiplicative. These are very restrictive properties. - Londonproperty

So $ f $ is both additive and multiplicative. These are very restrictive properties. - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 5Question: A philosopher of science ponders the rotational symmetry of a circular model representing fundamental particles, where the angle $ \theta $ satisfies $ \cos(3\theta) = \cos(2\theta) $ in the interval $ [0, 2\pi) $. Find the sum of all such angles $ \theta $.

📌 Solution: We begin with the equation:

📌 \cos(3\theta) = \cos(2\theta)

📌 Using the identity $ \cos A = \cos B $ implies $ A = 2k\pi \pm B $ for some integer $ k $, we apply it here:

📌 3\theta = 2k\pi \pm 2\theta

📌 We consider two cases:

📌 Case 1:** $ 3\theta = 2k\pi + 2\theta $

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