How do you evaluate $tan ((2pi)/3)$ ?

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Answer 1 · 2016-12-04T03:53:48

$tan((2pi)/3)=-sqrt3$

$tan((2pi)/3)$

Recall the identity $tantheta=sintheta/costheta$

According to the unit circle,

$sin((2pi)/3)=sqrt3/2$ and $cos((2pi)/3)=-1/2$

$tan((2pi)/3) =frac{sin((2pi)/3)}{cos((2pi)/3)}=frac(sqrt3/2)(-1/2)$

$=sqrt3/2 * -2/1=sqrt3/cancel2 * -cancel2/1=-sqrt3$

How do you evaluate tan ((2pi)/3)tan ((2pi)/3)?