Unformatted text preview: Limagon: _r=a:bcose
r=atbsin0 ‘(0<a,0<b) Rose C urves n petals if n is odd
2:: petals if n is even
(I! Z 2) ' C ircles and
Lemniscates Special l’olar Graphs um
um a a a a  — = <  < 2  a 2
b < l b l I b b
Limacon with Cardioid Dimpled (Eonvex
inner loop (heart sh:lped) limacon lnmacon ur: .1
2 r=acosn9 r=acosn8 r=asinne Rose curve Rose curve Rose curve Rose curve MN E
2 a
 2 ._ 2
r=ac059 r=asin9 r3=azsm26 r —a c0529
Circle Circle Lemniscare Lemmscate Test for Symmetry in Polar (oordinales The graph of a. polar equation is symmetric with respect to the following if the
given substitution yields an equivalent equation. 1. The line 9 =. 1r/2: Replace (r, 0) by (r, 1r  0) or (—r, ‘9)
2. The polar ans: Replace (r, 0) by (r. 9) or (—r, 1r  9).
3. The pole: Replace (r, 0) by (r. 1r + 9) or (r. 9). r = asinnO ...
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 Spring '08
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 Calculus

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