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

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

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

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

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## Comments

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TopNewestOh wow, that is a surprising bound.

(Using Wolfram) Equality holds at \( x \approx 0.12408 \). – Calvin Lin Staff · 1 year, 10 months ago

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– Cody Johnson · 1 year, 10 months ago

Better approximation: \(x\approx0.12407932542544436\)Log in to reply

– Daniel Liu · 1 year, 9 months ago

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".Log in to reply