How do you evaluate cot (4pi/3)?

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Answer 1 · 2015-10-18T06:29:06

$cot((4pi)/3)=sqrt3/3$

$(4pi)/3$ is a special angle.

$cot((4pi)/3)$

$=(cos((4pi)/3))/(sin((4pi)/3))$

$=[(-1/2)]/[(-sqrt3/2)]$

$=(-1/cancel2)*(-cancel2/sqrt3)$

$=1/sqrt3*sqrt3/sqrt3$

$=color(red)(sqrt3/3)$