(573,#85) a) Investigate the family of curves defined by the polar equations , where n is a positive integer. How is the number of loops related to n?
b)What happens if the equation , is replaced by ?

Solution:

For odd values of n, the number of loops is identical to the value of n.

For n=1, For n=3,

For n=5,

For even values of n, the number of loops is twice the value of n.

For n=2, For n=4,

For n=6,

If the equation is replaced by the absolute value of the function, the number of loops are always twice the value of n

For n=1, For n=2,
For n=3, For n=4,

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by:sh