First we get the rectangular equation of the circle.
The center is the polar point, which is
That's the point that we get when we
1. swing counter-clockwise
radians or 90°
from the right side of the x-axis, and
2. Go out 1 unit in that direction, which
turns out to be directly upward.
So that's the same point as the rectangular point (0,1)
So the circle with that center and a radius of
is this
black circle:
which has rectangular equation:
which becomes
or
Then to change from rectangular to polar or
vice-versa we draw this:
From which we see that
,
, and
So we replace the x2+y2 by r2 and
the y using
solved for y,
So the rectangular equation
becomes
the polar equation:
Edwin