The standard equation for a circle in
rectangular coordinates with center (h,k)
and radius r is:



Substitute h=0, k=-4, and r=4









Now we draw a typical angle  in standard 
position. Unfortunately the software here can't
get the Greek letter theta, so I'll use "phi" instead. 



Write down the trig equation for the sine,
cosine, and and the Pythagorean theorem:



Solve the first two equations for 
y and x:



Now go back to this equation:



Notice we can replace the first two
terms  by 
and we get:



Now we can replace  by






Factor out r:



, 

The first equation can be ignored. It is
just the equation of the origin (pole).
But the circle contains the origin (pole).
So we end up with:



Edwin