Graph r(t) = <t^2, cos t, sin t>

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Discussion Overview

The discussion centers around graphing the parametric curve defined by the function r(t) = . Participants explore the characteristics of the curve, including its range and behavior in different coordinate planes, while seeking assistance with graphing tools.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants seek a graphing program to visualize the curve defined by r(t).
  • There is a suggestion that the curve represents a circular motion in the y-z plane while extending along the x-axis.
  • One participant proposes that the implied range for x is greater than 0, with y and z constrained between -1 and 1, and describes how to find the 2D projections in the coordinate planes.
  • Another participant agrees with the constraints of the curve being confined to a unit cylinder in the y-z plane as it progresses along the x-axis.
  • Some participants discuss the possibility of needing a larger range for the graph, with one asserting that the stated range is maximal in the y and z directions.
  • There is a clarification that while the range in y and z is maximal, it is possible to extend the x range significantly to visualize the curve better.
  • Confusion arises regarding the interpretation of "larger range," with participants attempting to clarify their positions on the matter.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the range for the graph, with some asserting the maximal nature of the range in y and z, while others suggest that extending the x range can enhance the visualization of the curve. The discussion remains unresolved regarding the extent of the range and its implications.

Contextual Notes

Participants rely on assumptions about the behavior of the curve based on the parametric equations, and there are unresolved aspects regarding the exact nature of the range and its graphical representation.

crazynut52
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r(t)= <t^2, cost, sint>

Does anyone have a graphing program to make a picture of this, thanks.
 
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crazynut52 said:
r(t)= <t^2, cost, sint>

Does anyone have a graphing program to make a picture of this, thanks.

What kind of range are you looking for?

I assume this is a vector field?
 
its a curve of that function. I'm not sure on the range, I guess just enough to show the pattern. I believe it is a cos sin circle coming out the x axis.
 
Try this:

http://graphical.shacknet.nu/image1.jpg
 
Last edited by a moderator:
The implied range is that x>0, and that y and z must both be between -1 and 1 (inclusive). I don't have a graphing utility handy, but what I would do is find the 2D curve in each coordinate plane by eliminating the parameter. So, in the xy plane, you have y(x)=arccos(x1/2), in the xz plane you have z(x)=arcsin(x1/2), and in the yz plane you have y2+z2=1.

Basically, the curve is constrained to the unit cylinder y2+z2=1, and as it goes around it moves forward on the x-axis, starting from x=0.
 
Tom Mattson said:
The implied range is that x>0, and that y and z must both be between -1 and 1 (inclusive). I don't have a graphing utility handy, but what I would do is find the 2D curve in each coordinate plane by eliminating the parameter. So, in the xy plane, you have y(x)=arccos(x1/2), in the xz plane you have z(x)=arcsin(x1/2), and in the yz plane you have y2+z2=1.

Basically, the curve is constrained to the unit cylinder y2+z2=1, and as it goes around it moves forward on the x-axis, starting from x=0.

My plot seems to agree.
 
If you need a larger range, just request it.
 
graphic7 said:
If you need a larger range, just request it.

There is no larger range. The implied range that I stated is the maximal range.
 
Tom Mattson said:
There is no larger range. The implied range that I stated is the maximal range.

Only in the y and z directions, though. I just replotted from 0 to 1000 and you really get to see the unit cyclinder take form.
 
Last edited:
  • #10
graphic7 said:
Only in the y and z directions, though. I just replotted from -1000 to 1000 and you really get to see the unit cyclinder take form.

Ah, I see what you're saying. You mean a larger range in your picture. What I was saying is that the range implied by the equations is the maximal range, and that if there is any modification to that range in the problem, it can only be smaller, not bigger.
 
  • #11
Tom Mattson said:
Ah, I see what you're saying. You mean a larger range in your picture. What I was saying is that the range implied by the equations is the maximal range, and that if there is any modification to that range in the problem, it can only be smaller, not bigger.

Ah, sorry for the confusion.
 

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