TRACING OF POLAR CURVES. 



dr _ a (0 cos 9 sin 6} 

 d6~ ~^~ - 1 



381 



sn 



tan 9 = 4 - -j - : z . 

 V cost) sin 8 



As r is never infinite there is no asymptote ; r is positive 

 from 6 = to 6 IT, negative from = IT to 6 = ZTT, and 

 so on. 



When 6 = 0, tan <f> assumes the form - ; on examination it 

 will be found infinite. 



The curve begins at A, crossing the initial line at right 



angles, since there tan <f> is infinite : as 6 changes from to IT 

 the portion ABO is traced out; as 6 changes from TT to 2?r 

 the portion ODEFO is traced out, and so on. The curve 

 forms an infinite number of loops, each smaller than the pre- 

 ceding and all passing through 0. 



If we ascribe negative values to 6 we obtain the dotted 

 part lying below the straight line OA. 



351. Trace the curve 



