Why's the Graph of $y = sin (cos (e^x))$ so Wonky?
$begingroup$
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.
$x = 8$, 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
edited 3 mins ago
YuiTo Cheng
2,40641037
asked 3 hours ago
John A. John A.
301213
$endgroup$
add a comment |
$begingroup$
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.
$x = 8$, 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
edited 3 mins ago
YuiTo Cheng
2,40641037
asked 3 hours ago
John A. John A.
301213
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
$x = 8$, 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
edited 3 mins ago
YuiTo Cheng
2,40641037
asked 3 hours ago
John A. John A.
301213
$endgroup$
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.
$x = 8$, 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
graphing-functions
edited 3 mins ago
YuiTo Cheng
2,40641037
asked 3 hours ago
John A. John A.
301213
edited 3 mins ago
YuiTo Cheng
2,40641037
asked 3 hours ago
John A. John A.
301213
edited 3 mins ago
YuiTo Cheng
2,40641037
edited 3 mins ago
YuiTo Cheng
2,40641037
edited 3 mins ago
YuiTo Cheng
2,40641037
2,40641037
asked 3 hours ago
John A. John A.
301213
asked 3 hours ago
John A. John A.
301213
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
add a comment |
$begingroup$
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
add a comment |
2 Answers
2
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$begingroup$
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.
answered 3 hours ago
peterwhypeterwhy
12.1k21229
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add a comment |
$begingroup$
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.
answered 3 hours ago
Bruno EBruno E
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.
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2 Answers
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active
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2 Answers
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active
oldest
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oldest
votes
$begingroup$
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.
answered 3 hours ago
peterwhypeterwhy
12.1k21229
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
peterwhypeterwhy
12.1k21229
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
peterwhypeterwhy
12.1k21229
$endgroup$
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.
answered 3 hours ago
peterwhypeterwhy
12.1k21229
answered 3 hours ago
peterwhypeterwhy
12.1k21229
answered 3 hours ago
peterwhypeterwhy
12.1k21229
answered 3 hours ago
peterwhypeterwhy
12.1k21229
12.1k21229
add a comment |
add a comment |
$begingroup$
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.
answered 3 hours ago
Bruno EBruno E
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.
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
Bruno EBruno E
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.
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
Bruno EBruno E
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.
$endgroup$
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.
answered 3 hours ago
Bruno EBruno E
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.
answered 3 hours ago
Bruno EBruno E
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.
answered 3 hours ago
Bruno EBruno E
312
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.
add a comment |
add a comment |
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$begingroup$
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