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Home » Birthday Surprise Delivery Ideas You’ll Want to Share (Guaranteed to Impress!) - AMAZONAWS

Birthday Surprise Delivery Ideas You’ll Want to Share (Guaranteed to Impress!) - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 5Question: Among all solutions to $ \cos(3\theta) = \frac{\sqrt{3}}{2} $ in $ [0^\circ, 360^\circ] $, find the maximum value of $ \theta $ that corresponds to a resonance condition in a glaciological model of ice flow oscillations.

📌 We begin by solving the equation:

📌 \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

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