MAC 2312 FIU Find the Area of The Region Outside the Inner Loop Calculus Questions
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Group Worksheet/homework ue Thursday, Nov. 3, 2022
– MAC 2312, Fall 2022
1. Roses are curves given in polar coordinates by r = a cos(n?), or r = a sin(n?), where a is a constant (a )lation¦actor) and n is a positive integer related to the number of petals. When n is even, the rose has 2n-petals; when n
is odd, the rose has n-petals, but each petal is traced twice when 0 ? ? ? 2?.
(a) Make a table of values (?, r) and sketch (in the Cartesian coordinate system) the graph of the rose r = cos(3?)
and the graph of the rose r = sin(2?) (in separate graphs).
(b) Find the area enclosed by one petal of the rose r = cos(3?) and find the area of one petal enclosed by the rose
r = sin(2?).
2. (a) Make a table of values (?, r) and sketch (in the Cartesian coordinate system) the graph of the limacon with
inner loop r = 1 + 2 cos ?. Is the graph symmetrical with respect to any of the coordinate axis?
(b) Find the area enclosed by the inner loop (it may be most convenient to use symmetry).
(c) Find the area of the region outside the inner loop, but still inside the limacon.
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