<prompt> Je, grafu r 4 cos theta na r 8 sin theta hukatiza mara ngapi?  <response>: Kwa r 4 cos theta,anzaalignx r cos theta 4 cos2 theta 2 cos 2 theta 2, y r dhambi theta 4 dhambi theta cos theta 2 dhambi 2 theta.mwishoalignKwa hiyo,x - 22 y2 4 cos2 2 theta 4 sin2 2 theta 4.Hivyo, grafu ya r 4 cos theta ni mduara unaozingatia 2,0 na radius 2.Kwa r 8 sin theta,anzaalignx r cos theta 8 dhambi theta cos theta 4 dhambi 2 theta, y r dhambi theta 8 sin2 theta 4 - 4 cos 2 theta.mwishoalignKwa hiyo,x2 y - 42 16 sin2 2 theta 16 cos2 2 theta 16.Hivyo, grafu ya r 8 sin theta ni mduara unaozingatia 0,4 na radius 4.Kupanga miduara hii, tunapata kwamba inakatiza kwa pointi 2.asyukubwa wa kitengo 0.5 cm;jozi moo t halisi halisi r 4 cos t; kurudi rcost, rsint;njia foo moo0;t halisi;kwa t 0; t pi 0.1; t t 0.1 foo foo--moot;chorafoo,nyekundu;lebor 4 cos theta, 6.5,-1, nyekundu;jozi moo t halisi halisi r 8 dhambi t; kurudi rcost, rsint;njia foo moo0;kwa t 0; t pi 0.1; t t 0.1 foo foo--moot;kuchora foo, bluu;lebor 8 sin theta, 6.5,5, bluu;chora-6,0--6,0;chora0,-2--0,10;nukta 2,0;nukta 0,4;asy 