Next find the area inclosed in the intersection of the two graphs. Find all poin

Question

Next find the area inclosed in the intersection of the two graphs.

Find all points of intersection (r, theta) of the curves r=3cos( theta ), r = 5 sin ( theta ). Note: In this problem the curves intersect at the pole and one other point. Only enter the answer for nonzero r in the form (r, heta) with heta measured in radians. Next find the area inclosed in the intersection of the two graphs. Find all points of intersection ( r, theta) of the Lemniscate r2 = 9 cos(2 theta ), and the circle r = 1 for values of theta satisfying - pi / 2

Explanation / Answer

r = sin(?) ............ circle
r = sin(2?) .......... 4 leaf rose

sin(?) = sin(2?)
sin(?) (1 - 2cos(?)) = 0
? sin(?) = 0 ... ? = 0,?
? cos(?) = 1/2 ... ? = ?/3 (6k + 1) and ?/3 (6k + 5) { k ? ? }

Graphically (the circle and the rose intersect at 0

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