Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sine of inverse pi pattern
  1. Prime pattern (Replies: 4)

  2. Pi in binary (Replies: 9)

  3. Finding the pattern (Replies: 3)

  4. Randomness of pi (Replies: 24)

Loading...