How do you convert # X + Y = 0# to polar form?

1 Answer
A. S. Adikesavan
Apr 20, 2016

#r=0, theta=3pi/4 and theta=7pi/4#

Explanation:

#X=r cos theta and Y = r sin theta#.
So, X + Y = 0 becomes #r(cos theta + sin theta) = 0#.

The solutions are #r = 0 and cos theta + sin theta = 0#..

#So, tan theta = -1#. This gives two solutions in #[0, pi]#, as given in the answer.

Some niceties:

Note that, in polar coordinates, r = 0 gives the pole but #theta# = constant gives the half line from the pole in that direction, sans pole Pole is a point of discontinuity..
I think that I have given justification for giving three polar equations for the whole line represented by X + Y = 0, in rectangular coordinates.

I consider pole r = 0 as only the limit of r, upon reaching the end called pole (origin), along any radial line #theta# = constant. ..

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