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January 14th, 2015, 06:06 PM  #1 
Newbie Joined: Jan 2015 From: Queens Posts: 8 Thanks: 0  Parameterization of curves. Very confused
I'm having problems with these questions. I remember learning cos^2t+sin^2t=1. Can that help me for three dimensions? How do I know if it's a circle or an ellipse or anything else? Sketch the following parameterized curves: r(t) = <4+2 cos(t), 7  2 sin(t)>, with t between 0 and pi. r(t)= <2t,4+2t,3+t>, with t between 0 and 1. r(t) = <3 cos(t), t, 3 sin(t)>, for all t. Last edited by skipjack; January 16th, 2015 at 02:04 PM. 
January 15th, 2015, 05:20 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,338 Thanks: 532 
The first one looks like a semicircle, although missing a coordinate. The second is a straight line in space. The third is a helix (looks sort of like a spring).

January 15th, 2015, 07:16 PM  #3 
Newbie Joined: Jan 2015 From: Queens Posts: 8 Thanks: 0 
Can you show way values must be used for chart? Like chart values of x,y,z. Also, how do you draw it? Last edited by skipjack; January 16th, 2015 at 01:56 PM. 
January 16th, 2015, 01:47 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,338 Thanks: 532 
Choose a sequence of t values for each curve and compute (x,y,z). For the first two the t interval is finite, so use enough values to get a good picture. For the third subdivide $\displaystyle (0,2\pi)$ to get enough points to get the picture and then repeat a few times by adding $\displaystyle 2\pi$ to the previous interval. 

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calculus, confused, curves, math, parameterization 
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