Find the tangent of an angle $ heta $ on a unit circle

Given an angle $ \theta $ on a unit circle, the tangent of the angle is defined as the ratio of the sine to the cosine of the angle.

$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $

For instance, if $ \theta = \frac{\pi}{4} $:

$ \tan\left(\frac{\pi}{4}\right) = \frac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

Thus, the tangent of $ \frac{\pi}{4} $ is 1.

To find the tangent of an angle $ heta $ on a unit circle, use the formula:

$ an( heta) = frac{sin( heta)}{cos( heta)} $

If $ heta = frac{pi}{3} $:

$ anleft(frac{pi}{3}
ight) = frac{sinleft(frac{pi}{3}
ight)}{cosleft(frac{pi}{3}
ight)} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3} $

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

To find the tangent of an angle $ heta $ on a unit circle, use:

$ an( heta) = frac{sin( heta)}{cos( heta)} $

For example, if $ heta = frac{pi}{6} $:

$ anleft(frac{pi}{6}
ight) = frac{sinleft(frac{pi}{6}
ight)}{cosleft(frac{pi}{6}
ight)} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3} $

Hence, the tangent of $ frac{pi}{6} $ is $ frac{sqrt{3}}{3} $.

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