Why's the Graph of $y = sin (cos (e^x))$ so Wonky? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How to draw graph of this functionWhat is the equation for this graph?What's the graph for this periodic functionWhat is the function that generates this graph?Why can't this be the graph of any function?What is the function behind this graph?What kind of function is represented by this graph?What function created this graph and output?Can this set define the graph of this function?Help me finding function which give this type of graph.
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
Segmentation fault output is suppressed when piping stdin into a function. Why?
What is special about square numbers here?
Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?
Do warforged have souls?
Why does the Event Horizon Telescope (EHT) not include telescopes from Africa, Asia or Australia?
Did the new image of black hole confirm the general theory of relativity?
What information about me do stores get via my credit card?
How does ice melt when immersed in water?
What was the last x86 CPU that did not have the x87 floating-point unit built in?
Can a 1st-level character have an ability score above 18?
University's motivation for having tenure-track positions
Simulating Exploding Dice
Can withdrawing asylum be illegal?
Am I ethically obligated to go into work on an off day if the reason is sudden?
Who or what is the being for whom Being is a question for Heidegger?
In horse breeding, what is the female equivalent of putting a horse out "to stud"?
Simulation of a banking system with an Account class in C++
What can I do if neighbor is blocking my solar panels intentionally?
Didn't get enough time to take a Coding Test - what to do now?
I could not break this equation. Please help me
How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time
Did the UK government pay "millions and millions of dollars" to try to snag Julian Assange?
Was credit for the black hole image misattributed?
Why's the Graph of $y = sin (cos (e^x))$ so Wonky?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How to draw graph of this functionWhat is the equation for this graph?What's the graph for this periodic functionWhat is the function that generates this graph?Why can't this be the graph of any function?What is the function behind this graph?What kind of function is represented by this graph?What function created this graph and output?Can this set define the graph of this function?Help me finding function which give this type of graph.
$begingroup$
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
$endgroup$
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
$endgroup$
$begingroup$
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
$endgroup$
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
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
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
active
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.
$endgroup$
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.
New contributor
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3186818%2fwhys-the-graph-of-y-sin-cos-ex-so-wonky%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
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.
$endgroup$
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.
$endgroup$
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.
$endgroup$
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
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.
New contributor
$endgroup$
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.
New contributor
$endgroup$
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.
New contributor
$endgroup$
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.
New contributor
New contributor
answered 3 hours ago
Bruno EBruno E
312
312
New contributor
New contributor
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3186818%2fwhys-the-graph-of-y-sin-cos-ex-so-wonky%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
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