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9/23/2016 2:09:54 AM
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I'm a high school senior in Honors Calc II. Could you please explain, in terms that I'd understand, why it is not pi over 2?
English
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Have you covered Fourier series yet?
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I don't believe so. We did some stuff with series analysis and sums last year, but the name Fourier hasn't come up yet.
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Edited by The Cellar Door: 9/23/2016 12:51:53 PMWell, that's okay, I'll try to explain it simply. These^ are the first two terms. Im guessing you're familiar with integration, so you understand what the integral is. In this situation, the "y" value will decrease as more of these sin(x/a)/(x/a) are tacked on and a increases (think of how sin and y are related). When "y" is smaller than "x," the result is slightly different from π/2. Because of how many terms it takes for this to happen, the change is very minuscule.
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Edited by humanbeing1701: 9/27/2016 9:21:26 PMYeah that all makes sense. I suppose I should've phrased the question better: How does one look at the problem that you typed out and identify that the next term is not pi/2? The given problem does not inherently suggest that the terms are integrals, so how would one identify that they are solutions to integrals and how would one figure out what integral they came from?
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You should assume integrals of trigonometric functions will be used when you're dealing with sequences that have pi in them.
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Ah. I assume that the reason for this will become clear as I learn more about sequences?
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Well, yea, but for now, just think about it intuitively, what will give you a value which contains π no matter what you input? A trigonometric function. At least, in radians that is. Which, in turn, means, if you're summing a sequence of trigonometric functions, you're still going to get a value which contains π, because all you are doing is taking values which contain π and relating them to other values with the same property.
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Hmm alright, that makes sense. Thanks for all your help!
