Mixing
Why do the graphs of $y=operatorname{arccot}(x)$ and $y=arctan(1/x)$ only agree for $x>0$?
$begingroup$
When trying to plot a graph of $y=operatorname{arccot}(x)$, a function which I do not know the appearance of, I would try and get it in terms of something I do know:
$$y=operatorname{arccot}(x)$$
$$x=cot(y)$$
$$frac1x=tan(y)$$
$$y=arctanleft(frac1xright)$$
However, when using an online graph plotter, only the $x>0$ region is correct. Why would this be?
functions
edited Jan 19 at 13:21
Blue
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
$endgroup$
add a comment |
$begingroup$
When trying to plot a graph of $y=operatorname{arccot}(x)$, a function which I do not know the appearance of, I would try and get it in terms of something I do know:
$$y=operatorname{arccot}(x)$$
$$x=cot(y)$$
$$frac1x=tan(y)$$
$$y=arctanleft(frac1xright)$$
However, when using an online graph plotter, only the $x>0$ region is correct. Why would this be?
functions
edited Jan 19 at 13:21
Blue
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
$endgroup$
1
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05
add a comment |
$begingroup$
When trying to plot a graph of $y=operatorname{arccot}(x)$, a function which I do not know the appearance of, I would try and get it in terms of something I do know:
$$y=operatorname{arccot}(x)$$
$$x=cot(y)$$
$$frac1x=tan(y)$$
$$y=arctanleft(frac1xright)$$
However, when using an online graph plotter, only the $x>0$ region is correct. Why would this be?
functions
edited Jan 19 at 13:21
Blue
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
$endgroup$
When trying to plot a graph of $y=operatorname{arccot}(x)$, a function which I do not know the appearance of, I would try and get it in terms of something I do know:
$$y=operatorname{arccot}(x)$$
$$x=cot(y)$$
$$frac1x=tan(y)$$
$$y=arctanleft(frac1xright)$$
However, when using an online graph plotter, only the $x>0$ region is correct. Why would this be?
functions
functions
edited Jan 19 at 13:21
Blue
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
edited Jan 19 at 13:21
Blue
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
edited Jan 19 at 13:21
Blue
48.6k870156
edited Jan 19 at 13:21
Blue
48.6k870156
edited Jan 19 at 13:21
Blue
48.6k870156
48.6k870156
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
asked Jan 19 at 13:17
Henry LeeHenry Lee
2,054219
2,054219
1
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05
add a comment |
1
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05
1
1
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
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');
});
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%2f3079347%2fwhy-do-the-graphs-of-y-operatornamearccotx-and-y-arctan1-x-only-agre%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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');
});
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%2f3079347%2fwhy-do-the-graphs-of-y-operatornamearccotx-and-y-arctan1-x-only-agre%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');
});
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');
});
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');
});
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
1
$begingroup$
See math.stackexchange.com/questions/304399/…
$endgroup$
– lab bhattacharjee
Jan 19 at 14:05