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Home » From 5/6 to a Decimal: This Never-Again Conversion Changes Everything! - Abbey Badges

From 5/6 to a Decimal: This Never-Again Conversion Changes Everything! - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 f(x) = rac{1 - \cos 2x}{2} + rac{1 + \cos 4x}{2} = rac{1}{2} - rac{\cos 2x}{2} + rac{1}{2} + rac{\cos 4x}{2} = 1 - rac{\cos 2x}{2} + rac{\cos 4x}{2}

📌 f(x) = 1 + rac{1}{2}(\cos 4x - \cos 2x)

📌 Now, use the identity for $ \cos 4x - \cos 2x $:

📌 \cos A - \cos B = -2 \sin\left(rac{A+B}{2}

📌 ight)\sin\left(rac{A-B}{2}

📌 Let $ A = 4x $, $ B = 2x $:

📌 \cos 4x - \cos 2x = -2 \sin(3x)\sin(x)

📌 f(x) = 1 + rac{1}{2}(-2 \sin 3x \sin x) = 1 - \sin 3x \sin x

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