Given any Cartesian coordinates, (x,y), there are polar coordinates with
Find polar coordinates with for the following
Cartesian coordinates:
(a) If then
,
,
(b) If then
,
,
(c) If then
,
,
(d) If then
,
,
(e) If then
,
,
(f) If then
,
.

(a) 9.22
, 1.35
(b)
17.46
, 0.23
(c)
see work
, -0.51
(d)
16.40
, 0.66
(e)
see work
, -1.35
(f)
-2
, see work

A curve in polar coordinates is given by:
Point P is at
1) Find polar coordinate r for P, with r > 0 and
r =
2) Find cartesian coordinates for point P.
x =
, y =
3) How may times does the curve pass through the origin when

A circle C has center at the origin and radius 9.
Another circle K has a diameter with one end at the origin
and the other end at the point (0,16).
The circles C and K intersect in two points. Let P be the point of
intersection of C and K which lies in the first quadrant.
Let be the polar coordinates
of P, chosen so that r is positive and
Find r and . r =