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Vector Functions

  • Thread starter Sastronaut
  • Start date
  • #1
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Homework Statement


Graph the curve with the parametric equations

x=√(1-0.25cos^2(10t)) * cost
y=√(1-0.25cos^2(10t)) * sint
z=0.5cos10t

explain the appearance of the graph by showing that it lies on a sphere


Homework Equations





The Attempt at a Solution


could anyone please just point me in the right direction on how to start this problem? any help would be greatly appreciated! thanks pf!
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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'Graph the curve' seems pretty straightforward. Did you do that?

Did you manipulate the parametric equations for x, y, and z to see if you can obtain the equation of a sphere?

That would be pretty conclusive if you did.
 
  • #3
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A sphere is the set of points equidistant from the same point. If a sphere has radius R, what equation in x,y,z describes it? Take the x, y, z you were given, with the assorted sines and cosines and see what happens when you plug those variables into the equation of a sphere.

As far as graphing, I am a lousy artist, but if I had to graph it I'd sketch 3-d coordinates and graph some points based on cartesian x, y and z. This is maybe cheating, but I can't think too well in terms of cos 10t. The 10t will turn out to be irrelevant anyway-- try paragraph 1 and you'll see.
 
  • #4
68
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thank you brmath and steamking! brmath...that's exactly what I am trying now. I am plugging in x, y, and z into the equation of a sphere and seeing if my t's cancel and the equation is satisfied.
 

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