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

1 Answer

Dec 4, 2016

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

Explanation:

#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#

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