How do you find the exact value of $cot ((7pi)/4)$ ?

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Answer 1 · 2015-05-30T21:37:30

On the trig unit circle,

$cot ((7pi)/4) = 1/tan ((7pi)/4)$

$tan ((7pi)/4) = tan (- pi/4 + 2pi)$ (same terminal)
$tan (- pi/4 + 2pi) = tan (- pi/4) = - tan (pi/4) = - 1$

$cot ((7pi)/4) = 1/tan = (1/-1) = -1$

How do you find the exact value of cot ((7pi)/4)cot ((7pi)/4)?