Find the value of $ an(frac{pi}{4}) $ on the unit circle

To find the value of $ \tan(\frac{\pi}{4}) $ on the unit circle, we use the definition of tangent, which is the ratio of sine to cosine:

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

At $ \theta = \frac{\pi}{4} $, both $ \sin(\frac{\pi}{4}) $ and $ \cos(\frac{\pi}{4}) $ are equal to $ \frac{\sqrt{2}}{2} $:

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

To find the value of $ an(frac{pi}{4}) $ on the unit circle, use:

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

At $ heta = frac{pi}{4} $, we have:

$ an(frac{pi}{4}) = 1 $

To find $ an(frac{pi}{4}) $:

$ an(frac{pi}{4}) = 1 $

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