SOLUTION: find the rectangle coordinates of the polar point -5, 5pi/2

This one is better done graphically than algebraically:

To plot the polar point (r,), start at the rectangular point
(0,r). Think of a radius drawn from the origin to that point on the x-
axis.  That's the green line on the graph below connecting the origin 
to the rectangular point (x,y) = (-5,0)

That is, we start with a radius r = x = -5 on the x-axis at the rectangular 
point (-5,0) like this:



 is  which means it is 5 right angles, 
or 5 90-degree angles.

So we swing the green line counter-clockwise through the 
angle  (five 90° angles, or  revolutions,
indicated by the curved red line below:



So the green radius ended up with its tip at the rectangular point (0,-5).

So the polar point (r,) = (-5,) is the exact same 
point as the rectangular point (x,y) = (0,-5).

Edwin