query: Value of $x$ in floor Inequality: $\lfloor \sin^{-1}(x)\rfloor >\lfloor \cos^{-1}(x)\rfloor$
positive_passages.docid: 16337
positive_passages.text: Find the solution of $\lfloor \sin^{-1}(x)\rfloor>\lfloor \cos^{-1}(x)\rfloor$
negative_passages.docid: 146023
negative_passages.text: How to prove that $x^2 - \lfloor x\rfloor^2$ is onto?
negative_passages.docid: 102580
negative_passages.text: How to solve an definite integral of floor valute function?
negative_passages.docid: 45728
negative_passages.text: Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
negative_passages.docid: 17285
negative_passages.text: Proof of greatest integer theorem: floor function is well-defined
negative_passages.docid: 28125
negative_passages.text: Showing that $1 - \frac{x^2}2\leq\cos x$, $\forall x \in \mathbb{R}$
negative_passages.docid: 76828
negative_passages.text: Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
negative_passages.docid: 78528
negative_passages.text: Trigonometric fraction Inequality question
negative_passages.docid: 94658
negative_passages.text: Computing $\text{lim}_{n \rightarrow \infty}\frac{n!}{n^{\lfloor y\sqrt{n} \rfloor}(n-\lfloor y \sqrt{n}\rfloor)!}$
negative_passages.docid: 25883
negative_passages.text: Calculating $\Big\lfloor\underbrace{\sqrt{2017+\sqrt{2017+...+\sqrt{2017}}}}_\text{2017 roots}\Big\rfloor$
negative_passages.docid: 5222
negative_passages.text: $\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
negative_passages.docid: 19791
negative_passages.text: Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$
negative_passages.docid: 129890
negative_passages.text: Proving inequality $|\sin(n\theta) |\le n\sin\theta$
negative_passages.docid: 96791
negative_passages.text: How to show that $\lfloor n/1\rfloor+\lfloor n/2 \rfloor+....+\lfloor n/n\rfloor+\lfloor{\sqrt{n}}\rfloor$ is even?
negative_passages.docid: 5934
negative_passages.text: How to prove floor identities?
negative_passages.docid: 52029
negative_passages.text: If $x\in\mathbb R$, solve $4x^2-40\lfloor x\rfloor+51=0$.
negative_passages.docid: 13098
negative_passages.text: Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$