How do you evaluate $tan (\frac{2 π}{3})$ $tan ((2pi)/3)$ ?

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How do you evaluate $tan (\frac{2 π}{3})$ $tan ((2pi)/3)$ ?

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Answer 1 · 2016-12-04T03:53:48

$tan (\frac{2 π}{3}) = - \sqrt{3}$ $tan((2pi)/3)=-sqrt3$

Explanation:

$tan (\frac{2 π}{3})$ $tan((2pi)/3)$

Recall the identity $tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$

According to the unit circle,

$sin (\frac{2 π}{3}) = \frac{\sqrt{3}}{2}$ $sin((2pi)/3)=sqrt3/2$ and $cos (\frac{2 π}{3}) = - \frac{1}{2}$ $cos((2pi)/3)=-1/2$

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

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

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How do you evaluate $tan (\frac{2 π}{3})$ $tan ((2pi)/3)$ ?

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