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Math Help - Question 1

  1. #1
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    Question 1

    Find the range of the function,
    y=sin(sin(sin(sin(sin x))))
    Last edited by ThePerfectHacker; December 5th 2006 at 12:47 PM.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    The rules is that you post thy answers in white.
    Failure to follow these rules will result in excommunication.

    Find the range of the function,
    y=sin(sin(sin(sin(sin x))))
    Just a question about the rules. Do you just want the answer, or do you want a proof for these as well?

    -Dan
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    Quote Originally Posted by topsquark View Post
    Just a question about the rules. Do you just want the answer, or do you want a proof for these as well?

    -Dan
    Post anything that helps obtain a solution.


    This is mine 28th post!!!
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    Quote Originally Posted by ThePerfectHacker View Post
    The rules is that you post thy answers in white.
    Failure to follow these rules will result in excommunication.

    Find the range of the function,
    y=sin(sin(sin(sin(sin x))))
    Radians or degrees?
    ----
    EDIT (Responce from ThePerfectHacker):
    In radians
    Last edited by ThePerfectHacker; October 11th 2006 at 04:15 AM.
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    The graph of the sine curve is progressively flattening out each sin( that you add. One may hypothesize that the curve is approaching zero.

    The range is clearly between y = -1 .. 1, although I am not sure of the exact values.
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    Quote Originally Posted by Glaysher View Post
    Radians or degrees?
    ----
    EDIT (Responce from ThePerfectHacker):
    In radians
    At least at one level it is irrelevant what angle measure is
    used.

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    At least at one level it is irrelevant what angle measure is
    used.

    RonL
    There is a big difference between radians and degrees to my thinking.

    Answer: Range(Y)= [-0.6275, 0.6275]
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    How so? Why does it matter when determining the range. Perhaps you are thinking of the domain, although in this situation that is irrelevant, too.
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    Quote Originally Posted by Random333 View Post
    There is a big difference between radians and degrees to my thinking.

    Answer: Range(Y)= [-0.6275, 0.6275]
    Supose that in this case the range were expresible in the form:

    [-tan(tan(7)), +tan(tan(7)]

    while this may numerically be a different range depending on whether we are
    in degrees or radians, the most elegant form of the answer does not care
    two hoots about which angle mode we use.

    A more interesting question about this problem might be what is the domain?
    There are two natural assumptions one could make for the domain, and they
    are R and C. Each of these assumptions gives rise to a different answer,
    and each is equally plausible as a guess at the setters intention. If I were
    solving this problem I would solve both of these possibilities.

    RonL
    Last edited by CaptainBlack; October 14th 2006 at 10:47 PM.
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    Quote Originally Posted by CaptainBlack View Post
    Supose that in this case the range were expresible in the form:

    [-tan(tan(7)), +tan(tan(7)]

    while this may numerically be a different range depending on whether we are
    in degrees or radians, the most elegant form of the answer does not care
    two hoots about which angle mode we use.

    A more interesting question about this problem might be what is the domain?
    There are two natural assumptions one could make for the domain, and they
    are R and C. Each of these assumptions gives rise to a different answer,
    and each is equally plausible as a guess at the setters intention. If I were
    solving this problem I would solve both of these possibilities.

    RonL
    Then is answer simply:

    [-sin(sin(sin(sin(1)))), sin(sin(sin(sin(1))))?

    Because that seems too simple to be right. I was trying to think of a way of writing it exactly in terms of pi

    EDIT: Correction - Typed too many sines!
    Last edited by Glaysher; October 14th 2006 at 11:51 PM. Reason: Correction
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    Quote Originally Posted by Glaysher View Post
    Then is answer simply:

    [-sin(sin(sin(sin(sin(1))))), sin(sin(sin(sin(sin(1)))))?

    Because that seems too simple to be right. I was trying to think of a way of writing it exactly in terms of pi
    Or [sin(sin(sin(sin(1)))), sin(sin(sin(1)))]?

    sin[0,2pi] = [-1,1],
    sin[-1,1] = [sin(1),1],
    sin[sin(1),1] = [sin(sin(1)),sin(1)],
    sin[sin(sin(1)),sin(1)] = [sin(sin(sin(1))),sin(sin(1))],
    sin[sin(sin(sin(1))),sin(sin(1))] = [sin(sin(sin(sin(1)))),sin(sin(sin(1)))].
    Last edited by JakeD; October 14th 2006 at 11:32 PM.
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    Quote Originally Posted by JakeD View Post
    Or [sin(sin(sin(sin(1)))), sin(sin(sin(1)))] ?

    sin[0, 2pi] = [-1,1],
    sin[-1,1] = [sin(1),1],


    for theta in the range [-pi/2, pi/2] sin is monotonic increasing so:

    sin([-1,1]) = [sin(-1), sin(1)] = [-sin(1), sin(1)]


    RonL
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    Member Glaysher's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    for theta in the range [-pi/2, pi/2] sin is monotonic increasing so:

    sin([-1,1]) = [sin(-1), sin(1)] = [-sin(1), sin(1)]


    RonL
    Did you check mine after I corrected it as I had originally typed too many sines?
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  14. #14
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    Quote Originally Posted by Glaysher View Post
    Did you check mine after I corrected it as I had originally typed too many sines?
    Yes I did, and it agrees with what I think the solution for the real
    domain should be. However I'm not the setter of this problem, nor have I
    discussed it with him so I don't know what he thinks a correct solution would
    look like

    RonL

    (who thinks the quoting in this thread is too complex for white
    text - you would not believe how messy some of my posts
    have been while sorting out the quoted and reply text)
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    Quote Originally Posted by Glaysher View Post
    Then is answer simply:

    [-sin(sin(sin(sin(1)))), sin(sin(sin(sin(1))))?
    I agree also, that's how I came up with my answer of:
    Quote Originally Posted by Random333 View Post
    Answer: Range(Y)= [-0.6275, 0.6275]
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