# Find the exact value. tan(6pi)

Find the exact value.
$\mathrm{tan}\left(6\pi \right)$
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minotaurafe
$\mathrm{tan}\left(6\pi \right)=\mathrm{tan}\left(3\left(2\pi \right)\right)$
$=\mathrm{tan}\left(2\pi \right)=\mathrm{tan}0=0$
$\mathrm{tan}\left(k\ast 2\pi \right)=0$ for k=0,1,2,3,4,....(multiples of $2\pi$ )
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Francisco Proctor
An identity states that $\mathrm{tan}\theta =\mathrm{tan}\left(\theta ±2\pi n\right)$,where n is an integer, as with any other trig function.
So,$\mathrm{tan}\left(6\pi \right)=\mathrm{tan}\left(0+2\pi \left(3\right)\right)=\mathrm{tan}\left(0\right)=0$ from the unit circle.