282 



PRACTICAL MATHEMATICS 



To draw the curve, give some well-known values and calculate 

 the corresponding values of r. 



Y 



FIG, 92. 



The curve is evidently symmetrical about the horizontal axis, 

 and therefore the whole area will be twice the area of the top half. 



Area = 



(l-cos0) 2 d0 



(1 - 2 cos + cos 2 0) 



L - 2 cos + 

 - 2 sin + 



1 + cos 2 



7 sin 201' 

 4 J 



Since 



r 2 + 



r = 0(1 cos 0) 



dr 



jz = a sin 

 at) 



^ = a 2 (l - 2 cos + cos 2 + sin 2 0) 

 = 2a 2 (l - cos 0) 



