Visualizing a Parametric Equation in 3D Space

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Homework Help Overview

The discussion revolves around visualizing a parametric equation in 3D space, specifically the equations x=2, y=sin(t), and z=cos(t). Participants are exploring the geometric interpretation of these equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand whether the given equations describe a sphere or a circle. There is a discussion about the implications of x being a constant value and how that affects the dimensionality of the shape represented by the equations.

Discussion Status

Some participants have expressed confusion regarding the nature of the shape described by the equations, with one suggesting it might be a line due to the single degree of freedom in the parameter t. There is no explicit consensus on the correct interpretation yet, as differing views are being explored.

Contextual Notes

Participants are questioning the assumptions about the geometric representation based on the constant value of x and the implications of the parametric equations.

CourtneyS
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Homework Statement


Given the eqn x=2, y=sin(t), z=cos(t), draw this function in 3-space.

Homework Equations


ABOVE^

The Attempt at a Solution


I did this:
x^2+y^2+z^2=2^2+(sin(t))^2+(cos(t))^2=5
Therefore we get x^2+y^2+z^2=5
Which is the eqn of a sphere with radius root5.

My friend said it's supposed to be a circle but I can't see how?
Which one of us is right if either.
 
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If x is always equal to 2, how can it be a sphere?
 
phyzguy said:
If x is always equal to 2, how can it be a sphere?
:(
 
CourtneyS said:
:(
Another way of looking at it... there is only one degree of freedom (t), so it must be a line, not a surface.
 

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