How can a sine function be transformed to have flat peaks? [duplicate]












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  • What is the approximation equation for making the day/night wave

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I'm trying to create a sine function that will fit a geochron clocks day/night line. Right now I just started with a simple sine function, using map coordinates, which is this y=69sin(x-15)+2 but the peaks of the function should be flat which was not achieved with this function. Any advice on how to relatively easily transform the function to get this effect?



This is the online geochron clock that I was looking at http://www.fourmilab.ch/cgi-bin/Earth






trigonometry







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marked as duplicate by Chris Culter, Lord Shark the Unknown, Shailesh, Cheerful Parsnip, KReiser Jan 3 at 4:36


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • $begingroup$
    What do you mean by flat?
    $endgroup$
    – Robert Israel
    Jan 2 at 18:50
















0












$begingroup$



This question already has an answer here:




  • What is the approximation equation for making the day/night wave

    1 answer




I'm trying to create a sine function that will fit a geochron clocks day/night line. Right now I just started with a simple sine function, using map coordinates, which is this y=69sin(x-15)+2 but the peaks of the function should be flat which was not achieved with this function. Any advice on how to relatively easily transform the function to get this effect?



This is the online geochron clock that I was looking at http://www.fourmilab.ch/cgi-bin/Earth






trigonometry







share|cite|improve this question









$endgroup$



marked as duplicate by Chris Culter, Lord Shark the Unknown, Shailesh, Cheerful Parsnip, KReiser Jan 3 at 4:36


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • $begingroup$
    What do you mean by flat?
    $endgroup$
    – Robert Israel
    Jan 2 at 18:50














0












0








0





$begingroup$



This question already has an answer here:




  • What is the approximation equation for making the day/night wave

    1 answer




I'm trying to create a sine function that will fit a geochron clocks day/night line. Right now I just started with a simple sine function, using map coordinates, which is this y=69sin(x-15)+2 but the peaks of the function should be flat which was not achieved with this function. Any advice on how to relatively easily transform the function to get this effect?



This is the online geochron clock that I was looking at http://www.fourmilab.ch/cgi-bin/Earth






trigonometry







share|cite|improve this question









$endgroup$





This question already has an answer here:




  • What is the approximation equation for making the day/night wave

    1 answer




I'm trying to create a sine function that will fit a geochron clocks day/night line. Right now I just started with a simple sine function, using map coordinates, which is this y=69sin(x-15)+2 but the peaks of the function should be flat which was not achieved with this function. Any advice on how to relatively easily transform the function to get this effect?



This is the online geochron clock that I was looking at http://www.fourmilab.ch/cgi-bin/Earth





This question already has an answer here:




  • What is the approximation equation for making the day/night wave

    1 answer







trigonometry




trigonometry






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asked Jan 2 at 18:44









L. MonusL. Monus

81




81




marked as duplicate by Chris Culter, Lord Shark the Unknown, Shailesh, Cheerful Parsnip, KReiser Jan 3 at 4:36


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by Chris Culter, Lord Shark the Unknown, Shailesh, Cheerful Parsnip, KReiser Jan 3 at 4:36


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • $begingroup$
    What do you mean by flat?
    $endgroup$
    – Robert Israel
    Jan 2 at 18:50


















  • $begingroup$
    What do you mean by flat?
    $endgroup$
    – Robert Israel
    Jan 2 at 18:50
















$begingroup$
What do you mean by flat?
$endgroup$
– Robert Israel
Jan 2 at 18:50




$begingroup$
What do you mean by flat?
$endgroup$
– Robert Israel
Jan 2 at 18:50










1 Answer
1






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oldest

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You could just use min and max to cut off the function at the top and bottom. If $alpha$ is the minimum value and $beta$ the maximum then try



$$
y(x) = min(max(Acos(k(x-x_0))+c,alpha ) , beta)
$$



for appropriate values of $A$, $k$, $x_0$, $c$, $alpha$, $beta$, where
begin{gather}
A>0
\
k>0
\
c-A<alpha<beta<c+A
end{gather}
If you want the flat regions to all be the same length then you should have
$$
c=frac{alpha+beta} {2}
$$
Note that I have used $cos$ so that $x_0$ is solar noon.






share|cite|improve this answer









$endgroup$




















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    You could just use min and max to cut off the function at the top and bottom. If $alpha$ is the minimum value and $beta$ the maximum then try



    $$
    y(x) = min(max(Acos(k(x-x_0))+c,alpha ) , beta)
    $$



    for appropriate values of $A$, $k$, $x_0$, $c$, $alpha$, $beta$, where
    begin{gather}
    A>0
    \
    k>0
    \
    c-A<alpha<beta<c+A
    end{gather}
    If you want the flat regions to all be the same length then you should have
    $$
    c=frac{alpha+beta} {2}
    $$
    Note that I have used $cos$ so that $x_0$ is solar noon.






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      You could just use min and max to cut off the function at the top and bottom. If $alpha$ is the minimum value and $beta$ the maximum then try



      $$
      y(x) = min(max(Acos(k(x-x_0))+c,alpha ) , beta)
      $$



      for appropriate values of $A$, $k$, $x_0$, $c$, $alpha$, $beta$, where
      begin{gather}
      A>0
      \
      k>0
      \
      c-A<alpha<beta<c+A
      end{gather}
      If you want the flat regions to all be the same length then you should have
      $$
      c=frac{alpha+beta} {2}
      $$
      Note that I have used $cos$ so that $x_0$ is solar noon.






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        You could just use min and max to cut off the function at the top and bottom. If $alpha$ is the minimum value and $beta$ the maximum then try



        $$
        y(x) = min(max(Acos(k(x-x_0))+c,alpha ) , beta)
        $$



        for appropriate values of $A$, $k$, $x_0$, $c$, $alpha$, $beta$, where
        begin{gather}
        A>0
        \
        k>0
        \
        c-A<alpha<beta<c+A
        end{gather}
        If you want the flat regions to all be the same length then you should have
        $$
        c=frac{alpha+beta} {2}
        $$
        Note that I have used $cos$ so that $x_0$ is solar noon.






        share|cite|improve this answer









        $endgroup$



        You could just use min and max to cut off the function at the top and bottom. If $alpha$ is the minimum value and $beta$ the maximum then try



        $$
        y(x) = min(max(Acos(k(x-x_0))+c,alpha ) , beta)
        $$



        for appropriate values of $A$, $k$, $x_0$, $c$, $alpha$, $beta$, where
        begin{gather}
        A>0
        \
        k>0
        \
        c-A<alpha<beta<c+A
        end{gather}
        If you want the flat regions to all be the same length then you should have
        $$
        c=frac{alpha+beta} {2}
        $$
        Note that I have used $cos$ so that $x_0$ is solar noon.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 2 at 22:23









        EddyEddy

        884612




        884612















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