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.
