A weird expression

Calculus Level 3

What is the value of the following expression?

sin % % % \lfloor \frac{\sin \%}{\% \ \%} \rfloor

Note: The % \% is in radians.


The answer is 99.

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1 solution

Jake Lai
May 5, 2015

% = 0.01 \% = 0.01

sin % % lim x 0 sin x x = 1 \frac{\sin \%}{\%} \approx \lim_{x \rightarrow 0} \frac{\sin x}{x} = 1

sin % % % 1 % = 100 \frac{\sin \%}{\% \ \%} \approx \frac{1}{\%} = 100

x > 0 sin x < x sin % % % 99.99 x > 0 \longrightarrow \sin x < x \therefore \frac{\sin \%}{\% \ \%} \approx 99.99\ldots

sin % % % = 99 \therefore \lfloor \frac{\sin \%}{\% \ \%} \rfloor = 99

Really? Level 4?

Jake Lai - 6 years ago

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It's 500% now

Joel Yip - 5 years, 4 months ago

Nice problem and solution. It pretty takes a crutial attention on the floor sign!

Math Mediocre - 5 years, 9 months ago

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