Find the value of $ an( heta) $ when $ heta $ is at the angle $ frac{pi}{4} $ on the unit circle

To find the value of $ \tan(\theta) $ when $ \theta $ is at the angle $ \frac{\pi}{4} $ on the unit circle, we use the definition of tangent in terms of sine and cosine:

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

At $ \theta = \frac{\pi}{4} $, we know:

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

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

So:

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

To find $ an( heta) $ at $ heta = frac{pi}{4} $ on the unit circle, we use:

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

Given:

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

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

Then:

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

The value of $ an( heta) $ at $ heta = frac{pi}{4} $ is:

$ frac{sin(frac{pi}{4})}{cos(frac{pi}{4})} = 1 $

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