Section 11-I Polar Coordinates / Graphs

I. To convert from polar coordinates to rectangular coordinates

     

    

II. To convert from rectangular coordinates to polar

      

     

        If  is in the same quadrant as the point (x, y), then r is positive. If  is in the opposite

        quadrant as the point (x,y), then r is negative.
 

III. When graphing polar equations:

        1. Test for symmetry

            (a)  Replace (r, ) by (r, ) or (-r, 

            (b) Polar axis: Replace (r, ) by (r, -) or (-r, )

            (c) Pole: Replace (r, ) by (r, ) or (-r, )

        2. Find the  value for which |r| is maximum.

        3. Find the  value for which r = 0.

        4. Know the different types of polar graphs.
 
 
(a) Limacons

(b) Rose Curves: n

(c) Circles

(d) Lemniscates