TIIK /'o/N/ /\ >/ 



ml. i ( 1"| luces to eq. [ i J. If thr lines are . 

 ^0=0, and eq. [1UJ reduces to 



MM *, * * 4 eat A, c* fc + * ti * Yt 0. [ U J 



207. Transformation of coordinates; rectangular systems. 

 nxl in An. -"_' t.i exist between rectangu- 

 lar and polar coordinate*! of a point may be used as fonnulas 



ill t.i thr other if till* or: 



i*le, and the reference axes are coinri.I.-m . Two other 

 >\e tnin.Hfurn may be useful, ( 1 ) from one set of 



rectangular axes to a parallel set, that is a l..m-. 

 oriyi oin one set of rectangular axe to 



:MT st-t tliroii^li tin- same origin, !.., a cliange of direc- 

 tion ot axes. Thru any transformation between rectangular 

 and polar systems can be \ 



ied by a comhinatiun uf 

 these three elementary trans- 

 lations. 

 ( 1 ) Change qf origin only. 



II IK- til. 



i 



.lit j^ 



. t- S* 

 of any 



0* = (A, Ar, .?); then, const nut- / J 

 th.- i.M.r.linates of any 

 /' \\ith reference to 

 i set of coordinate planes, it is evident, by analogy with 



71. ih.it 



= ?* + *, * = **+*, = **+./. . . . 



1 ) Change of n of ajree. Let a second set of ree- 



i axes, O.\ <>} < .luection angle* ,, 



,. 7r f S- ^r 7r all(l "r /^r 7r respectively, with the old 

 axes CLY, . 



