<prompt> Pata mlingano wa asymptote ya grafu ya r cos 2 theta sec theta.  <response>: Kwa r cos 2 theta sec theta,x r cos theta cos 2 thetanay r sin theta fraccos 2 theta sin thetacos theta.asyukubwa wa kitengo 1.5 cm;r halisi, t, x, y;t -0.4pi;r cos2tcost;x rcost;y r dhambit;njia foo x,y;kwa t -0.4pi; t 0.4pi; t t 0.01 r cos2tcost; x rcost; y r dhambit; foo foo--x,y;chorafoo,nyekundu;chora-1,-2.5---1,2.5,bluu dashed;chora-1.5,0--1.5,0;chora0,-2.5--0,2.5;asytheta inapokaribia fracpi2 kutoka chini, x cos 2 theta inakaribia -1 na y fraccos 2 theta sin theta cos theta inakaribia -infty. Kwa hivyo, mlinganyo wa asymptote ni x -1. 