

TRANSFORMATION OF t<nn;l>l V .1 TK& 



131 





(2) Sam* a* (1) *jvr/ ' line OR maJcn an 



iint/le ic trifA thf spirit. It is at 

 once evident th.it tin- f..riini!.i- 

 i t liis cane n 



+ ), J 



+ ). I 



ami y p8in(^ 



M f'Tiniilas fr this 

 a:.- : 



-' 



(8) Transformation from any Carte nan tyttcm to any j 



m. TruiiNt'nrm :.-. t. infill, ir a\rs \\lmsr nri^in is 



tin- i>rii|Kwecl p<>l in acuoin 71 ami 78. 



I'.'i-nnil.i | _'T ]..;[_".' ] ; i in t-nn from tho rectangular 

 teaian to the polar coordinates. 



EXERCISES 



following to the corresponding polar equation*: -I raw a 

 figure showing the two related systems of axes in each case. Take the pole 

 at tin- origin, the polar axis coincident with the axU of z, in exercises 1 



1 i*4-^=o. 3 J +j = 0(r-y*). 



2. >r - ' - '2 ay = 0. 4. y = x tana. 



- >/3jf -- 2 = 0, taking pole at origin, polar axis making the 

 angle 60 with the x-axis. 



6 ; _ y _ 4 r - fl - M = 0, taking the pole at the point , 

 ami the polar axis parallel to the r-axw. 



mge the following to corresponding rectangular equations. Take 

 the origin at the pole and the x-axis coincident with the polar axis. 



7. p = o. 9. p a Hin'J0= 10. 



' a pco20 = a. 10 p = aaml>^. 



10 multiply by p 1 ftn.l inlMJtut.. '2 in Bc<*0 fr 

 0; the equation then beoomei p j in0co0. 



11. = toos6L 12. tf = 3taii->L>. 13 * cos = **. 



