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jake's 58 hotel islandia - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 But \(\sin^2 x \cos^2 x = rac{1}{4} \sin^2 2x\), so:

📌 = 5 + rac{4}{\sin^2 2x}

📌 Minimum occurs when \(\sin^2 2x\) is maximized, i.e., \(\sin^2 2x = 1\) when \(x = rac{\pi}{4}\)

📌 Then value is \(5 + 4 = 9\)

📌 Question: Find the range of the function \(f(x) = rac{2\sin x + 3}{\sin x + 2}\) as \(x\) ranges over all real numbers such that \(\sin x

📌 e -2\) (which is always true since \(\sin x \in [-1,1]\)).

📌 Solution: Let \(y = rac{2\sin x + 3}{\sin x + 2}\). Solve for \(\sin x\):

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