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December 18 Information
s = cos(a).sin(a)
What is the correct mathematical way to prove that the max value of s is when a= 1/4pi or 3/4pi radians? I went to take derivative but that makes it go around in circles :)--
Dacium (
talk)
03:59, 18 December 2007 (UTC)reply
It's not all – you'll have to solve an equation, which in turn requires you to recall (or find in trig. tables) such value(s) which give , which may be (a little) harder than recalling cosine's
zeros. :) --
CiaPan (
talk)
09:33, 19 December 2007 (UTC)reply
You can do this with calculus, but it's easier to use geometry. Your function gives the area of a rectangle inscribed in a circle of radius 1/2 such that the angle between the base and the diagonal is a. The area is maximized by an inscribed square.
Yes it is. It's not easy, though - After several failed attempts, I have written a program to find a solution. Would you like me to present a solution, or do you want to try again now that you know it is possible? --
Meni Rosenfeld (
talk)
10:24, 18 December 2007 (UTC)reply
Exact, I got the same but reflected and rotated. It wasn't that hard, actually, took me 10 minutes of attempts. I got it by trying to understand how to minimize the impact of 4 cats on the board, getting three mice correctly placed and finally adding the fifth cat and moving one of the three mice. Before attempting it, speeding up your trial-and-error process with "tricks" is also useful. --
Taraborn (
talk)
13:49, 18 December 2007 (UTC)reply
As nobody else answers, I'll give a try. I suppose that it is called so because it is "too good to be true": the argument of the integral and the summands of the series are very similar, almost as if you could substitute sums for integrals. For similar reasons, somebody calls "freshman's dream" the congruence . It makes true what normally is not: being able to distribute exponents with respect to a sum.
Goochelaar (
talk)
15:40, 19 December 2007 (UTC)reply
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
current reference desk pages.
December 18 Information
s = cos(a).sin(a)
What is the correct mathematical way to prove that the max value of s is when a= 1/4pi or 3/4pi radians? I went to take derivative but that makes it go around in circles :)--
Dacium (
talk)
03:59, 18 December 2007 (UTC)reply
It's not all – you'll have to solve an equation, which in turn requires you to recall (or find in trig. tables) such value(s) which give , which may be (a little) harder than recalling cosine's
zeros. :) --
CiaPan (
talk)
09:33, 19 December 2007 (UTC)reply
You can do this with calculus, but it's easier to use geometry. Your function gives the area of a rectangle inscribed in a circle of radius 1/2 such that the angle between the base and the diagonal is a. The area is maximized by an inscribed square.
Yes it is. It's not easy, though - After several failed attempts, I have written a program to find a solution. Would you like me to present a solution, or do you want to try again now that you know it is possible? --
Meni Rosenfeld (
talk)
10:24, 18 December 2007 (UTC)reply
Exact, I got the same but reflected and rotated. It wasn't that hard, actually, took me 10 minutes of attempts. I got it by trying to understand how to minimize the impact of 4 cats on the board, getting three mice correctly placed and finally adding the fifth cat and moving one of the three mice. Before attempting it, speeding up your trial-and-error process with "tricks" is also useful. --
Taraborn (
talk)
13:49, 18 December 2007 (UTC)reply
As nobody else answers, I'll give a try. I suppose that it is called so because it is "too good to be true": the argument of the integral and the summands of the series are very similar, almost as if you could substitute sums for integrals. For similar reasons, somebody calls "freshman's dream" the congruence . It makes true what normally is not: being able to distribute exponents with respect to a sum.
Goochelaar (
talk)
15:40, 19 December 2007 (UTC)reply