\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2005e.02389}
\itemau{Fung, David; Ligh, Steve}
\itemti{Trigonometric representation of $\lbrack$x$\rbrack$.}
\itemso{Bogacki, Przemyslaw (ed.), Proceedings of the 7th annual international conference on technology in collegiate mathematics, ICTCM 7, Orlando, FL, USA, November 17--20, 1994. Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics (ISBN 0-201-87020-7). Electronic paper (1994).}
\itemab
In the software DERIVE (version 2.07), the greatest integer function, $\lbrack$x$\rbrack$, when simplified, is given as $\lbrack$x$\rbrack$ = arctan(cot(pi*x))/pi + x - 1/2. The above equality can be proved by means of properties of trigonometric functions. Using other inverse trigonometric functions, we obtain several forms for $\lbrack$x$\rbrack$ as well as other step-like functions. (authors' abstract) (The paper is available under http://archives.math.utk.edu/ICTCM/abs/7-FB17.html)
\itemrv{~}
\itemcc{I25 R25}
\itemut{greatest integer function; applications of mathematics to mathematics; trigonometric functions; proofs; computer algebra}
\itemli{}
\end