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\frac9!4! \cdot 3! \cdot 2! - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \cos(3\theta) = \frac{\sqrt{3}}{2}

📌 The general solution for $ \cos \phi = \frac{\sqrt{3}}{2} $ is:

📌 \phi = 30^\circ + 360^\circ k \quad \text{or} \quad \phi = 330^\circ + 360^\circ k, \quad k \in \mathbb{Z}

📌 Since $ \phi = 3\theta $, we substitute:

📌 3\theta = 30^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 10^\circ + 120^\circ k

📌 3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110^\circ + 120^\circ k

📌 We now find all $ \theta \in [0^\circ, 360^\circ] $ by plugging integer values of $ k $.

📌 For $ \theta = 10^\circ + 120^\circ k $:

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