Wikipedia:Reference desk/Archives/Mathematics/2006 September 29

Mixed trig / linear terms
Is there an algebraic method for finding solutions to equations of the form ax + bsin(x) + c = 0 ? Maelin 10:50, 29 September 2006 (UTC)


 * I don't think so. One special case would be $$\cos x = x$$ (almost, anyway), and there is no clean way to solve that, as far as i know. —Bromskloss 11:38, 29 September 2006 (UTC)


 * There's probably a way using the series definitions of the trig functions. ☢  Ҡ i∊ ff   ⌇  ↯  11:59, 29 September 2006 (UTC)


 * No, that won't help. Replacing the trigonometric function with an infinite series just gives you an equation where one side is an infinite series. This doesn't simplify the problem. It would help if you could do some manipulation on the series and find that the result is a series for some other known function that provides an algebraic solution, but in this case the series is just the sine series with a few terms altered, and that doesn't help. Fredrik Johansson 15:35, 29 September 2006 (UTC)


 * I am almost certain that (except for special cases) it will be impossible to find a closed expression for the solutions in terms of a finite combination of elementary functions like exponentials, sin, cos, tan, (and inverse trig functions) log, exp, or hyperbolic functions. I suspect that the best you will get (other than a numerical answer to a certain degree of accuracy) will be an infinite series expansion by using the Lagrange inversion theorem. Madmath789 12:28, 29 September 2006 (UTC)


 * I think that there isn't. If there was a way, then you could construct a cos(1) angle with compass and straightedge; but http://en.wikipedia.org/wiki/Angle_trisection. Sorry, maybe in the morning my brain will work, so I can give you the exact proof.

Functor nOOb200.65.178.127 07:45, 30 September 2006 (UTC)

data
data and graphs from 1990 to 2005 of the following South African macroeconomic variables: Real GDP, Inflation, Unemployment and Balance of payments


 * The above is not a question, and is not about mathematics, the topic of this reference desk. --Lambiam Talk  12:57, 29 September 2006 (UTC)


 * Hello! You should be able to post your question in another ref. desk page, as the misc. one. And please remember that no mechanical nor computerized parts are tortured to answer you question, we're not googols ;-)
 * So the title of the question might give : South A. macroeconomics, and the question could start with "hello, where may I find ...". Now, try this link first : South Africa. Thank you. -- DLL .. T 19:16, 29 September 2006 (UTC)

Economic Bundles
I've solved an equation for a bundle that includes 4 of unit X and 2.5 of unit Y as the utility-maximizing one. How come it is okay to have non-whole numbers as part of an answer...its not like I can go out an actually buy 2 and a half bananas!


 * Because mathematicians care more about number than whether it possible to have 2.4 children. More seriously, there are many applications where it is useful to have fractional results. So its good practice to start using them now as it will help you a lot in the future. --Salix alba (talk) 21:36, 29 September 2006 (UTC)


 * Just multiply by 2, then you have 8 of unit X and 5 of unit Y. StuRat 21:45, 29 September 2006 (UTC)


 * There are also applications where the solution must need be in whole numbers; anything else is totally useless. That is why there is the whole area of integer programming in the field of operations research. However, this is much and much harder. --Lambiam Talk  22:55, 29 September 2006 (UTC)