Find the tangent of angle $frac{pi}{3}$ using the unit circle.

To find the tangent of angle $\frac{\pi}{3}$ using the unit circle, we need to find the coordinates of the point where the terminal side of the angle intersects the unit circle.

For the angle $\frac{\pi}{3}$, the coordinates on the unit circle are $(\frac{1}{2}, \frac{\sqrt{3}}{2})$. The tangent of an angle is given by the ratio of the y-coordinate to the x-coordinate.

$\tan\left(\frac{\pi}{3}\right) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

Therefore, the tangent of $\frac{\pi}{3}$ is $\sqrt{3}$.

The tangent of an angle $ heta$ on the unit circle is the ratio of the y-coordinate to the x-coordinate of the point where the terminal side of $ heta$ intersects the unit circle.

For the angle $frac{pi}{3}$, the coordinates are $(frac{1}{2}, frac{sqrt{3}}{2})$. Hence,

$ ext{tan}left(frac{pi}{3}
ight) = frac{ ext{y-coordinate}}{ ext{x-coordinate}} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3}.$

So, $ anleft(frac{pi}{3}
ight) = sqrt{3}$.

For $ heta = frac{pi}{3}$, the unit circle coordinates are $(frac{1}{2}, frac{sqrt{3}}{2})$. Thus,

$ anleft(frac{pi}{3}
ight) = frac{ ext{y}}{ ext{x}} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3}.$

Therefore, $ anleft(frac{pi}{3}
ight) = sqrt{3}$.

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