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Guilherme's Numerical Inequalities - I

Let \( c \) be the Champernowne's constant, or\( c = 0.123456789101112131415161718192021... \)

Show, without calculator aid, that \[ \sin(c) + \cos(c) + \tan(c) > 10c \]

Note by Guilherme Dela Corte
2 years, 7 months ago

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Oh wow, that is a surprising bound.

(Using Wolfram) Equality holds at \( x \approx 0.12408 \). Calvin Lin Staff · 2 years, 7 months ago

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@Calvin Lin Better approximation: \(x\approx0.12407932542544436\) Cody Johnson · 2 years, 7 months ago

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@Calvin Lin I don't see how exactly it is surprising. The 10 can be replaced with any arbitrary constant, and it would be a "cool bound". Daniel Liu · 2 years, 6 months ago

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