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Math Help - Graphs of sin and cos

  1. #1
    Senior Member Mukilab's Avatar
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    Graphs of sin and cos

    Hello I know the formula for a minimum point in a quadratic curve (-b/2a) but I've been faced with a graph of y=sinx and I need to find the coordinates of the maximum point.

    I've gussed at 45,90. Any help?
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    Quote Originally Posted by Mukilab View Post
    Hello I know the formula for a minimum point in a quadratic curve (-b/2a) but I've been faced with a graph of y=sinx and I need to find the coordinates of the maximum point.

    I've gussed at 45,90. Any help?
    Dear Mukilab,

    A sinosoidal curve is an oscillating curve, hence having infinite number of maximum points. But if you consider a particular domain, such as 0\leq{x}\leq{\pi} you will be able to find some maximum points in that domain. Maximum points occur when,

    x=........-\frac{3\pi}{2},\frac{\pi}{2},\frac{5\pi}{2},\frac{  9\pi}{2}..........

    Hence x=\frac{n\pi}{2}~where~n=........-7,-3,1,5,9,13,........

    And since -1\leq{\sin{x}}\leq{1} the maximum value of sinx is 1.

    Therefore one could write the coodinates of the maximum points as, \left(\frac{n\pi}{2},1\right)~when~n=.........,-7,-3,1,5,9,13..........

    Hope this will help you.
    Attached Thumbnails Attached Thumbnails Graphs of sin and cos-sp-1.png  
    Last edited by Sudharaka; June 6th 2010 at 06:29 AM.
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  3. #3
    Senior Member Mukilab's Avatar
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    I'm sorry, I don't understand at "Maximum points occur when

    Hence "

    and"Therefore one could write the coodinates of the maximum points as, "
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    Quote Originally Posted by Mukilab View Post
    I'm sorry, I don't understand at "Maximum points occur when

    Hence "

    and"Therefore one could write the coodinates of the maximum points as, "
    Dear Mukilab,

    Do you know that the maximum value of sinx is 1? And do you know that, sinx=1 when x=\frac{\pi}{2}?
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  5. #5
    Senior Member Mukilab's Avatar
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    Sorry for my rash answer, all those functions did my head in.

    I've looked at quite a few interactive graph plotters since then and I understand this:

    Take a and b as intergers
    acos(bx)

    a will make the minimum and maximum y points that interger (e.g. 3cos, max y=3, min=-3)

    b will make the peaks closer together, roughly halving it (cos2x has y=0 on 45, cosx has y=0 on 90)

    What I don't understand is how these interact.

    Common logic says 3cos2x should have a point at y=0 with coordinates 45,0 and a minimum point with coordinates 90,-3

    but its not true!
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  6. #6
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    Quote Originally Posted by Mukilab View Post
    What I don't understand is how these interact.

    Common logic says 3cos2x should have a point at y=0 with coordinates 45,0 and a minimum point with coordinates 90,-3

    but its not true!
    It is true. 3\cos{2x}=0~when~x=\frac{\pi}{4} and 3\cos{2x}=-3~when~x=\frac{\pi}{2}
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