How many times will tan x be equal to a series of its reciprocals?
I saw this problem on Twitter several months ago, and I loved it, but I never got around to recording it until now. Given an infinite series of the reciprocals of the powers of tangent, how often between -90º and 90º would we expect that series to intersect with the tangent curve itself?
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If we can be a little bit clever about evaluating our infinite series, being careful of course to note under what circumstances we can expect it to converge, then this turns into a relatively easy quadratic formula problem. I don't want to spoil it, but the golden ratio also makes a cameo.
#mathcontest #trigonometry #infiniteseries
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