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Home » We solve this system using the Chinese Remainder Theorem. - jntua results

We solve this system using the Chinese Remainder Theorem. - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A bioinformatician is analyzing a genomic sequence pattern and comes across the trigonometric equation \(\sin(2z) = \cos(z)\). Determine all angles \(z \in [0^\circ, 360^\circ]\) that satisfy this equation.

📌 We start with the given equation:

📌 \sin(2z) = \cos(z)

📌 Using the double angle identity for sine, \(\sin(2z) = 2\sin(z)\cos(z)\), we rewrite the equation:

📌 2\sin(z)\cos(z) = \cos(z)

📌 Assuming \(\cos(z)

📌 eq 0\), we can divide both sides by \(\cos(z)\):

📌 2\sin(z) = 1 \quad \Rightarrow \quad \sin(z) = rac{1}{2}

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