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Possible Duplicate:
Solving $2x - \sin 2x = \pi/2$ for $0 < x < \pi/2$

For fun, I was trying to solve this problem without doing calculus. After dinking around with it for a while, I came across the following term and don't quite know how to solve it without guessing:

$$a - \sin{(a)} = \frac{\pi}{2}$$

Where $a$ will be the angle of the chord that will allow me to solve for the height - in theory :)

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    I should plug this in as-is and see if either the sin or the angle disappears. I could see this turning in 4R/3Pi if I worked it through.2011-07-01
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    This is essentially the same equation as in the question here http://math.stackexchange.com/q/48865/29062011-07-01
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    Not quite, Sin(2a) implies a double angle theorm with more ways to changes the terms around. It's actually really close to the Sin(x) = 1 - x from (26538), which answers stated it was transdendal and guessing/iterating was the way to solve it. But, because the value we're playing with is a Pi multiple, I thought there might be a shortcut or two I wasn't aware of.2011-07-01
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    This is very closely related to solving $\cos x = x$ (see the duplicate thread in earlier comment) and also see this: [Dottie Number](http://mathworld.wolfram.com/DottieNumber.html)2011-07-01
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    @Michael look carefully and you will see that there are factors of two on both sides of the equation I linked so the are essentially the same. There is an interesting point that the two formulae arise in different ways, and suggest different methods of approach.2011-07-01
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    Guys, Re-open this as to my above additions and to the algebra error in the answer please! Ahh! The error was fixed. Still, note my new comments above.2011-07-01
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    What algebra error? Set your $a = 2x$ you get exactly the same equation as the one this is a duplicate of. And please don't remove the "possible duplicate" box by hand.2011-07-01
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    By the way, for future reference (or for immediate reference if you'd like), a better way to post "re-opening requests" is to do so over at http://meta.math.stackexchange.com/ When you do, please ask a new question requesting re-opening, with a link to the closed question, as well as why you think the question should be re-opened (for example, in this case you will need to explain why this particular question is not, in fact, a duplicate of the linked one). You will get many more views that way.2011-07-01

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