Problem with sprial!!

im now doing a programme to plot a spiral then i would let the user to draw in between the line of spiral to check if it gone out of the line how many times.
i had manage to plot the spiral already. so now i want to know how to check if it gone out of the line.

i had tot of first finding the angle of the user point,
using Math.atan(the y-axis/x-axis)

after got the angle we carry on from there. but im lost!
please help me....!
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