What is the exact value of $cot 210$ ?

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Answer 1 · 2015-05-21T05:06:20

On the trig unit circle:

$sin 210 = sin (30 + 180) = -sin 30 = -1/2$
$cos 210 = cos (30 + 180) = -cos 30 = (-sqrt3)/2$

$cot 210 = cos 210/sin 210 = [(-sqrt3)/2]:(-1/2) = sqrt3$

What is the exact value of cot 210cot 210?