# 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
3 years, 6 months ago

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Oh wow, that is a surprising bound.

(Using Wolfram) Equality holds at $$x \approx 0.12408$$.

Staff - 3 years, 6 months ago

Better approximation: $$x\approx0.12407932542544436$$

- 3 years, 6 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".

- 3 years, 5 months ago