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Sine of inverse pi pattern

  1. Jun 21, 2011 #1
    I have noticed something strange when you take the value of sin(pi*10^-n). It approaches pi*10^-n. I have attatched the file here.

    Attached Files:

  2. jcsd
  3. Jun 21, 2011 #2
    Hi dimension10! :smile:

    Your result can be generalized. Indeed, if x is small then

    [itex]\sin(x)\sim x[/itex]

    So for small values of x, we will have that x approximates sin(x) quite closely.

    The precise result is

    [itex]\lim_{x\rightarrow 0}{\frac{\sin(x)}{x}}=1[/itex]

    which can be proved by geometric methods. See http://www.khanacademy.org/video/proof--lim--sin-x--x?playlist=Calculus [Broken] to see how to derive the result.
    Last edited by a moderator: May 5, 2017
  4. Jun 21, 2011 #3
    So that just means that sin(0)/0=1, right?
    Last edited by a moderator: May 5, 2017
  5. Jun 21, 2011 #4
    No, not at all, since you cannot divide by 0. What

    [tex]\lim_{x\rightarrow 0}{\frac{\sin(x)}{x}}=1[/tex]

    mean is, if x is very close to 0 (but not equal to 0!!), then [itex]\frac{\sin(x)}{x}[/itex] comes very close to 1.
    Thus if x is very close to 0, then sin(x) comes very close to x!!

    The statement sin(0)/0 makes no sense, since division by 0 is not allowed!
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