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