Graph Vector Functions: Explaining Appearance of Graph on Sphere

[Sastronaut]

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!

 

[SteamKing]

'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.

 

[brmath]

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.

 

[Sastronaut]

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.