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Home » The radius \(r\) of the circle is half the diagonal: - Moon Smoking

The radius \(r\) of the circle is half the diagonal: - Moon Smoking

📅 May 16, 2026 👤 scraface

May 16, 2026

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Let $ x = 0 $: $ \sin^2 0 = 0 $, $ \cos^2 0 = 1 $, $ f(0) = 1 $. Formu...
$ x = rac{\pi}{2} $: $ \cos 2x = \cos \pi = -1 $, $ \cos 4x = \cos 2\...
But earlier we said $ f(x) = 1 - rac{1}{2}(\cos 2x - \cos 4x) $. When...
But we want **minimum**, not maximum. Can $ f(x) $ be less than 1?
Try $ x = rac{\pi}{4} $: $ \sin^2 x = \left(rac{\sqrt{2}}{2}
ight)^2 = rac{1}{2} $, $ 2x = rac{\pi}{2} $, $ \cos^2(2x) = \cos^2(...
But according to formula: $ f\left(rac{\pi}{4}
ight) = 1 - rac{1}{2}(\cos rac{\pi}{2} - \cos \pi) = 1 - rac{1}{2}(...
Can it be smaller? Try $ x $ such that $ \sin^2 x $ is small and $ \co...
Try $ x = rac

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