---- START NEW MESSAGE --- Received: from cherry.ease.lsoft.com [209.119.0.109] by dpmail10.doteasy.com with ESMTP (SMTPD32-8.05) id AF2DE84020E; Tue, 27 Jan 2004 19:40:29 -0800 Received: from PEAR.EASE.LSOFT.COM (209.119.0.19) by cherry.ease.lsoft.com (LSMTP for Digital Unix v1.1b) with SMTP id <15.00CC01A6@cherry.ease.lsoft.com>; Tue, 27 Jan 2004 22:40:21 -0500 Received: from MITVMA.MIT.EDU by MITVMA.MIT.EDU (LISTSERV-TCP/IP release 1.8e) with spool id 9648 for PICLIST@MITVMA.MIT.EDU; Tue, 27 Jan 2004 22:40:16 -0500 Received: from MITVMA (NJE origin SMTP@MITVMA) by MITVMA.MIT.EDU (LMail V1.2d/1.8d) with BSMTP id 6220; Tue, 27 Jan 2004 22:39:46 -0500 Received: from relay01.kbs.net.au [203.220.32.149] by mitvma.mit.edu (IBM VM SMTP Level 430) via TCP with ESMTP ; Tue, 27 Jan 2004 22:39:45 EST X-Comment: mitvma.mit.edu: Mail was sent by relay01.kbs.net.au Received: from [220.240.60.50] (helo=blackbox) by relay01.kbs.net.au with smtp (Exim 3.36 #2) id 1AlgYL-00074G-00 for PICLIST@MITVMA.MIT.EDU; Wed, 28 Jan 2004 14:39:46 +1100 References: <001301c3e53f$ad6ce0c0$0100a8c0@carlos98> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <029c01c3e550$705244d0$ed00a8c0@blackbox> Date: Wed, 28 Jan 2004 14:39:04 +1100 Reply-To: pic microcontroller discussion list Sender: pic microcontroller discussion list From: Eugene Rosenzweig Subject: Re: [OT:] Curves intersection To: PICLIST@MITVMA.MIT.EDU Precedence: list X-RCPT-TO: Status: U X-UIDL: 371856023 I do not know how to solve 1-x^2-sin(x)=0 without approximation. However, I have looked up on Google the Taylor series expansion for sin(x), which is sin(x) = x - x^3/3! + x^5/5! - x^7/7! + .... The equation for y=1-x^2 is upside-down quadratic intersecting at y=1 and x=1/-1 so, from visual inspection, sin(x) intersects it twice, once on positive x, between 0 and 1 and once on negative, somewhere not too far from x=-1. I took the first two terms of sin(x) series, substituted into the equality and ended up with cubic: 1-x^2-x+x^3/6=0 I cannot even remember how to solve cubics so I found this online solver http://www.1728.com/cubic.htm and three values for x. The first one doesn't make sense but the other two are the ones we need: x=0.63715 x=-1.3937 The positive x solution is very close but the negative one is not, due to approximation of sin(x). Adding terms to sin(x) approximation would improve that but I cannot find an online calculator to solve a quintic :-) I have also used a shareware plotting program graphmatica and that had a tool for finding intersections and came up with very similar results. ----- Original Message ----- From: "Carlos Marcano" To: Sent: Wednesday, January 28, 2004 12:34 PM Subject: [OT:] Curves intersection Hi all: I got to admit that I am struggling with something that I should know as an engineer. I need to find analitically the points of intersection of two curves, that is: I) y= 1-(x*x) II) y= sen(x) Normally that would be as simple as doing I=II and resolving but in this case the fact that II is a trigonometrical ecuation brings some issues to the resolution. Having 1 - (x*x) = sen(x) I can4t find a way to get the posible values for x. I could try a graphical solution but I want the analitical (i.e. numerical) solution. Any ideas? *Carlos* --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.572 / Virus Database: 362 - Release Date: 27/01/04 -- http://www.piclist.com hint: PICList Posts must start with ONE topic: [PIC]:,[SX]:,[AVR]: ->uP ONLY! [EE]:,[OT]: ->Other [BUY]:,[AD]: ->Ads -- http://www.piclist.com hint: PICList Posts must start with ONE topic: [PIC]:,[SX]:,[AVR]: ->uP ONLY! [EE]:,[OT]: ->Other [BUY]:,[AD]: ->Ads .