Vector Functions

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

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
Staff Emeritus
Homework Helper
'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.

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.

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.