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Home » The sum of the first \( n \) terms of an arithmetic sequence is 210, - Aurero

The sum of the first \( n \) terms of an arithmetic sequence is 210, - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 \boxed{-5}

📌 Question:** A biodiversity specialist is studying the periodic behavior of genetic expression modeled by the equation \(2\cos(2z) = \sqrt{3}\). Find the sum of all angles \(z \in [0^\circ, 360^\circ]\) that satisfy this equation.

📌 First, solve for \(\cos(2z)\):

📌 2\cos(2z) = \sqrt{3} \quad \Rightarrow \quad \cos(2z) = \frac{\sqrt{3}}{2}

📌 The general solutions for \(\cos(2z) = \frac{\sqrt{3}}{2}\) are:

📌 2z = 30^\circ + 360^\circ n \quad \text{or} \quad 2z = 330^\circ + 360^\circ n

📌 Divide by 2 to find \(z\):

📌 z = 15^\circ + 180^\circ n \quad \text{or} \quad z = 165^\circ + 180^\circ n

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