# polarc - Limagon_r=a:bcose r=atbsin0 ‘(0

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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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