POLAR FORMULAE. EXAMPLES. 311 



a a 



7. If r = a (1 - cos 6], then $ = - , p = 2a sin 3 r , and the 



i A 



9 

 polar subtangent = 2a sin 2 - tan - . 



M A 



2 



8. If r 2 cos 20 = a 2 , shew that sin <f> = . . 



r 



9. If r 2 = a 2 cos 20, shew that < = + 2ft 



2j| 



a 



10. If r = a sec 3 - } shew that the locus of Y is a parabola. 



See the figure in Art. 284. 



11. If r = a (1 + cos 0), shew that the locus of Y is deter- 



V 

 mined by r = 2a I cos 



\ . 



12. If r 2 = a 2 cos 20, shew that the locus of Y is determined 



v 2 / 20\ 

 by r 2 = a 2 (cos J . 



13. Shew that the curve r cos = a cos 20 has an asymptote 



having for its equation r cos = a. 



14. Shew that the curve (r a) sin = b has an asymptote 



having for its equation r sin = b. 



15. Determine the asymptotes of the curve r cos 20 = a. 



16. Determine the asymptotes of the curve 



r sin 40 = a sin 3ft 



