My Math Forum Parameterization of curves. Very confused

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 January 14th, 2015, 07:06 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)= <2-t,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 03:04 PM.
 January 15th, 2015, 06:20 PM #2 Global Moderator   Joined: May 2007 Posts: 6,438 Thanks: 562 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, 08:16 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 02:56 PM.
 January 16th, 2015, 02:47 PM #4 Global Moderator   Joined: May 2007 Posts: 6,438 Thanks: 562 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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