Question

= 7/2 Problem 5 [3 marks Calculate the area enclosed by all the four loops of the four leaved roses indicated in the figure below where r = cos(20), = 0

Answer 1

Date / / sol area We need to find the enclosed by all the four loops of a four - petal rose . Here r = cos 120 By about symmetric Test, it the ac- axis and is the symmetric y-aris Symmetric Test: A curve in polar coordinates is symmetric about the x-ary it renlacing o by -0 m its equation produces an equivalent equation and about the y-arcis if replacing o by to ] 0 = 1/2 -o = 1/4 Area in polar co-ordinates is to given by given by I Į ² do By symmetry , it is clear that the area in the first quadrant that is sweht out for oso = 1/4 is one - eighth of the total ara inside the rose.

Date / / Thus, A = 8/14 ļ r² do 4 cos²20 do 2 (T1/4 cos 40+ 1. do I cos 20 = 2205²0-11 (et cos 40).do 20+ sin 40 /4 2 do 2.0 t sint - 0 + sino 2 2 so, Required area Note: The figure is of r= sim 20 asked is of &= is I aq units given in the question and the question cos 2o.