The equation asinx+bcosx=c and a family of cyclic Heron quadrilaterals
| dc.creator | Zelator, Konstantine | |
| dc.date | 2008-04-22 | |
| dc.date.accessioned | 2026-07-07T09:34:13Z | |
| dc.date.available | 2026-07-07T09:34:13Z | |
| dc.description | In the beginning of this paper, we present the general solution to the trigonometric equation asinx+bcosx=c. After that, we focus on the case when a^2+b^2=c^2. In this case, the general solution is expressed in terms of the acute angle theta which satisfies tan(theta)=a/b+c .From the right trianle with leglengths a and b, and hypotenuse length c, we construct a cyclic quadrilateral within which the angle theta is illustrated.Then we examine the case when a,b,and c are integers;and we derive or construct a family of cyclic Heron quadrilaterals. These are quadrilaterals with integer sidelengths or edges, integer diagonal lengths, and integer area.Also these quadrilaterals have their four vertices lying on a circle. The said family of quadrilaterals, is a three parameter infinite family. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0804.3600 | |
| dc.identifier | http://arxiv.org/abs/0804.3600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159414 | |
| dc.subject | General Mathematics | |
| dc.subject | A005 | |
| dc.title | The equation asinx+bcosx=c and a family of cyclic Heron quadrilaterals | |
| dc.type | text |