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Home » San Mateo County Fair 2024: Exclusive Secrets Every Visitor Misses! - Abbey Badges

San Mateo County Fair 2024: Exclusive Secrets Every Visitor Misses! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: Find all angles $z \in [0^\circ, 360^\circ]$ that satisfy $\sin(2z) = \cos(z)$.

📌 Solution: Use identity $\sin(2z) = 2\sin z \cos z$. So:

📌 2\sin z \cos z = \cos z.

📌 2\sin z \cos z - \cos z = 0 \Rightarrow \cos z (2\sin z - 1) = 0.

📌 $\cos z = 0 \Rightarrow z = 90^\circ, 270^\circ$.

📌 $2\sin z - 1 = 0 \Rightarrow \sin z = rac{1}{2} \Rightarrow z = 30^\circ, 150^\circ$.

📌 All solutions in $[0^\circ, 360^\circ]$ are $z = 30^\circ, 90^\circ, 150^\circ, 270^\circ$.

📌 Check each:

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