An infinite spiral is constructed by starting at (0,0), moving 1 unit to the right, turning 90 degrees left and moving 1/2 unit, turning 90 degrees left and moving 1/3 unit, etc. as shown in the figure below. What are the coordinates of the point the spiral converges to?

More generally, suppose a spiral in constructed by starting at (0,0),
moving 1 unit to the right, turning *x* degrees left and moving 1/2
unit, turning *x* degrees left and moving 1/3 unit, etc. The figure
below shows the beginning of the spiral when *x* is 45 degrees.
Determine the coordinates of the point the spiral converges to as a
function of *x*.