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Math Help - Definition of Sin or Cos

  1. #1
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    Definition of Sin or Cos

    Where do sin and cos come from.

    I use them on my caluclator but I never really understand where they are getting the number from. My teacher keeps mentioning that when he was a student a hundred years ago they had to look up all of the values in a book.

    so where do the values come from. could I derive them myself?
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  2. #2
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    See MathWorld - Sine and MathWorld - Cosine.

    One can express Sine and Cosine in natural exponents or infinite series.
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  3. #3
    Junior Member theprof's Avatar
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    Quote Originally Posted by Math Dude
    Where do sin and cos come from.

    I use them on my caluclator but I never really understand where they are getting the number from. My teacher keeps mentioning that when he was a student a hundred years ago they had to look up all of the values in a book.

    so where do the values come from. could I derive them myself?
    For sure!
    There are formulas that do the work very well, but are quite difficult to explain expecially if you have not studied calculus.
    The name is Taylor's formula
    http://www.math.jhu.edu/courses/107/...es/node34.html

    But here is an example
    Be sure that your calculator shows RAD and calculate sin(0.1)
    you get something like
    0.09983341664

    Now try with this:
    x - x^3/6
    if you put 0.1 = 1/10 in place of x you get
    1/10 -1/6000 ~ 0.09983333333
    how many decimal digit are correct? Six!

    Better results (and longer calculation) are obtained if you use
    x^5/120 - x^3/6 + x
    0.1^5/120 - 0.1^3/6 + 0.1 ~ 0.09983341666
    Ten decimal digits are correct!
    They are long calculation to be made by hand, aren't they?

    Once matematicians made all by hand. Look at you calculator with more respect from now on

    bye
    Last edited by theprof; April 10th 2005 at 03:18 AM.
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