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January 14th, 2015, 06:06 PM   #1
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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 02:04 PM.
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January 15th, 2015, 05:20 PM   #2
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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).
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January 15th, 2015, 07:16 PM   #3
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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.
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January 16th, 2015, 01:47 PM   #4
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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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