Important Question from Trigonometry

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What is the general form of limacons and cardioids and how do you graph transformations?

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You can find a lot of information and easy explained stuff in “K. A. Stroud – Engineering Mathematics. MacMillan, p. 539, 1970”, such as:

jzbvL8CbSNGImYXMPeHL polar1

3iAgJidISnuzcENBvvuW polar2

If you want to plot them in Cartesian coordinates remember the transformation:

For example:
in the first one: r=asin(θ) choose various values of the angle θ evaluate the corresponding r and plug them into the transformation equations for x and y. Try it with a program such as Excel… it is fun!!!

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