Why's the Graph of $y = sin (cos (e^x))$ so Wonky?












1












$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










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$endgroup$












  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago
















1












$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










share|cite|improve this question











$endgroup$












  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago














1












1








1





$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










share|cite|improve this question











$endgroup$




I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!







graphing-functions






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share|cite|improve this question













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share|cite|improve this question








edited 5 mins ago









YuiTo Cheng

2,40641037




2,40641037










asked 3 hours ago









John A. John A.

301213




301213












  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago


















  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago
















$begingroup$
Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
$endgroup$
– Minus One-Twelfth
3 hours ago




$begingroup$
Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
$endgroup$
– Minus One-Twelfth
3 hours ago












$begingroup$
@MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
$endgroup$
– Saucy O'Path
3 hours ago




$begingroup$
@MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
$endgroup$
– Saucy O'Path
3 hours ago












$begingroup$
Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
$endgroup$
– Minus One-Twelfth
3 hours ago




$begingroup$
Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
$endgroup$
– Minus One-Twelfth
3 hours ago










2 Answers
2






active

oldest

votes


















1












$begingroup$

The software may be performing some sampling on $x$ values to plot your function.



When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






share|cite|improve this answer









$endgroup$





















    3












    $begingroup$

    That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






    share|cite|improve this answer








    New contributor




    Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      The software may be performing some sampling on $x$ values to plot your function.



      When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



      But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



      In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



      This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        The software may be performing some sampling on $x$ values to plot your function.



        When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



        But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



        In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



        This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          The software may be performing some sampling on $x$ values to plot your function.



          When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



          But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



          In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



          This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






          share|cite|improve this answer









          $endgroup$



          The software may be performing some sampling on $x$ values to plot your function.



          When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



          But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



          In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



          This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 3 hours ago









          peterwhypeterwhy

          12.1k21229




          12.1k21229























              3












              $begingroup$

              That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






              share|cite|improve this answer








              New contributor




              Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






              $endgroup$


















                3












                $begingroup$

                That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






                share|cite|improve this answer








                New contributor




                Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






                $endgroup$
















                  3












                  3








                  3





                  $begingroup$

                  That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






                  share|cite|improve this answer








                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  $endgroup$



                  That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.







                  share|cite|improve this answer








                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|cite|improve this answer



                  share|cite|improve this answer






                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  answered 3 hours ago









                  Bruno EBruno E

                  312




                  312




                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.





                  New contributor





                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






























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