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Polar Celebration

Graph this unusual polar function correctly and you will know why you were asked to do it!


r = |tan x|[1/|tan x|]
for 0 < x ≤ π



Question: Any idea how to change the equation so that "the result" would be inverted?

 

Source: American Mathematics Monthly, February 2008, p. 113

Hint: No hint needed....

 

Solution Commentary: I am not "heart"less, but feel no solution is needed.