The parametric equation of a cone $z = sqrt{x^{2} + y^{2}}$.
The given equation is -
$z = sqrt{x^{2} + y^{2}} , 0 le z le 1$
Let $x = r cos t$, $y = r sin t$ and $z = r$; where $0 le r le 1$
and $0 le t le 2 pi$.
Since $z$ is taken from $0$ to $1$ , so $r$ is also taken from $0$ to $1$
I didn't understand why $t$ is in between $0$ and $2 pi$?
calculus parametric
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
add a comment |
The given equation is -
$z = sqrt{x^{2} + y^{2}} , 0 le z le 1$
Let $x = r cos t$, $y = r sin t$ and $z = r$; where $0 le r le 1$
and $0 le t le 2 pi$.
Since $z$ is taken from $0$ to $1$ , so $r$ is also taken from $0$ to $1$
I didn't understand why $t$ is in between $0$ and $2 pi$?
calculus parametric
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
add a comment |
The given equation is -
$z = sqrt{x^{2} + y^{2}} , 0 le z le 1$
Let $x = r cos t$, $y = r sin t$ and $z = r$; where $0 le r le 1$
and $0 le t le 2 pi$.
Since $z$ is taken from $0$ to $1$ , so $r$ is also taken from $0$ to $1$
I didn't understand why $t$ is in between $0$ and $2 pi$?
calculus parametric
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
The given equation is -
$z = sqrt{x^{2} + y^{2}} , 0 le z le 1$
Let $x = r cos t$, $y = r sin t$ and $z = r$; where $0 le r le 1$
and $0 le t le 2 pi$.
Since $z$ is taken from $0$ to $1$ , so $r$ is also taken from $0$ to $1$
I didn't understand why $t$ is in between $0$ and $2 pi$?
calculus parametric
calculus parametric
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
edited Dec 11 '18 at 7:05
Nosrati
26.5k62354
26.5k62354
asked Dec 11 '18 at 5:13
Mathsaddict
2608
asked Dec 11 '18 at 5:13
Mathsaddict
2608
asked Dec 11 '18 at 5:13
Mathsaddict
2608
2608
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
At any given value of $r$ you get a value of $z,$ the height of the cone.
But a height and a value $r$ by themselves don't give you a cone. To have a cone you need a circular base. It will also have a circular cross section in any plane parallel to the base between the base and the apex.
Now review parametric formulas for a circle and see anything matches part of what you see here.
answered Dec 11 '18 at 5:51
David K
52.7k340115
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
add a comment |
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%2f3034916%2fthe-parametric-equation-of-a-cone-z-sqrtx2-y2%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
At any given value of $r$ you get a value of $z,$ the height of the cone.
But a height and a value $r$ by themselves don't give you a cone. To have a cone you need a circular base. It will also have a circular cross section in any plane parallel to the base between the base and the apex.
Now review parametric formulas for a circle and see anything matches part of what you see here.
answered Dec 11 '18 at 5:51
David K
52.7k340115
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
add a comment |
At any given value of $r$ you get a value of $z,$ the height of the cone.
But a height and a value $r$ by themselves don't give you a cone. To have a cone you need a circular base. It will also have a circular cross section in any plane parallel to the base between the base and the apex.
Now review parametric formulas for a circle and see anything matches part of what you see here.
answered Dec 11 '18 at 5:51
David K
52.7k340115
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
add a comment |
At any given value of $r$ you get a value of $z,$ the height of the cone.
But a height and a value $r$ by themselves don't give you a cone. To have a cone you need a circular base. It will also have a circular cross section in any plane parallel to the base between the base and the apex.
Now review parametric formulas for a circle and see anything matches part of what you see here.
answered Dec 11 '18 at 5:51
David K
52.7k340115
At any given value of $r$ you get a value of $z,$ the height of the cone.
But a height and a value $r$ by themselves don't give you a cone. To have a cone you need a circular base. It will also have a circular cross section in any plane parallel to the base between the base and the apex.
Now review parametric formulas for a circle and see anything matches part of what you see here.
answered Dec 11 '18 at 5:51
David K
52.7k340115
answered Dec 11 '18 at 5:51
David K
52.7k340115
answered Dec 11 '18 at 5:51
David K
52.7k340115
answered Dec 11 '18 at 5:51
David K
52.7k340115
52.7k340115
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
add a comment |
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
In the parametric formula of circle in $x-y$ plane, $x = r cos t$ and $y = r sin t$ . Where $t$ is the angle between $x$ axis and the position vector of point $(x,y)$. To make a complete circle, $t$ moves from 0 to $2pi$. So, in the formula of base of cone, which is a circle, $t$ should also move from 0 to $2pi$ to make the comlete base. Is this okay?
– Mathsaddict
Dec 11 '18 at 6:11
That is the right idea.
– David K
Dec 11 '18 at 12:15
That is the right idea.
– David K
Dec 11 '18 at 12:15
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3034916%2fthe-parametric-equation-of-a-cone-z-sqrtx2-y2%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
