• Home
• Volumes
• Authors
• Keywords
• Search

Electronic Proceedings of the Seventh Annual International Conference on Technology in Collegiate Mathematics Orlando, Florida, November 17-20, 1994 Paper C026 Trigonometric Representation of [x]

David Fung Department of Mathematics Southeastern Louisiana University Hammond, LA 70402 USA Phone: (504) 549-2175 FMAT1804@SELU.EDU

Steve Ligh Department of Mathematics Southeastern Louisiana University Hammond, LA 70402 USA Phone: (504) 549-2175 ligh@selu.edu list of all papers by this author

---

Click to access this paper: paper.pdf

---

ABSTRACT

In the software DERIVE (version 2.07), the greatest integer function, [x], when simplify, is given as

[x] = 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 [x] as well as other step-liked functions. Moreover, the above equality gives us, among other things, the indefinite integral of [x] as

(2x[x] - [x] - [x]^2)/2 + C.

---

Keyword(s): Derive, trigonometry, calculus, integrals