This is so important it deserves its own post!
Don't make the mistake of misjudging the period (when the graph repeats itself) of a polar graph.
For example: You'd kick yourself if you found out you got a problem wrong, because you thought the bounds were $0$ to $2\pi$ when it was actually $0$ to $\pi$. Or vice versa.
I'll try to get more information on parametric equations up, but I feel this was worth mentioning ASAP.
I have trouble determining the bounds for parametric problems. Any tips?
ReplyDeleteTry using the graph of $r$ as a function of $\theta$ to help you understand and/or draw the polar plot. See page 658 for two examples of sketching the curve.
DeleteNote that: $r=\cos(2n\theta)$ has an even number of leaves and has period $2\pi$ while $r=\cos([2n+1]\theta)$ has an odd number of leaves and has period $\pi$. What about the plot of $r$ as a function of $\theta$ makes this so?
See the following polar plots at Wolfram Alpha:
"Polar Plot" of $r=\cos(2\theta)$
"Cartesian Plot" of $r=\cos(2\theta)$
"Polar Plot" of $r=\cos(3\theta)$
"Cartesian Plot" of $r=\cos(3\theta)$
"Polar Plot" of $r=\sin(3\theta)$
I made two replies related to this on http://timothytran.blogspot.com/2012/02/class-discussion-due-20120228.html at "Stacey Hall" and "Chris.Skoff".
Professor Brown recently posted on the Facebook page regarding section 10.3. A link to the Facebook page is located on the right-hand side of this blog.
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