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

To find the tangent of the angle $ \theta $ on a unit circle, one must understand that the tangent of an angle is defined as the ratio of the sine to the cosine of that angle:

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

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

$ \sin(\frac{\pi}{4}) = \cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $

So:

$ \tan(\frac{\pi}{4}) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

To determine the tangent of angle $ heta $ on a unit circle, use the ratio of sine to cosine:

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

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

$ sin(frac{pi}{6}) = frac{1}{2} $

$ cos(frac{pi}{6}) = frac{sqrt{3}}{2} $

Thus:

$ an(frac{pi}{6}) = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{ sqrt{3}} = frac{ sqrt{3}}{3} $

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

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

Example for $ heta = 0 $:

$ sin(0) = 0 $

$ cos(0) = 1 $

$ an(0) = frac{0}{1} = 0 $

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