Find the tangent of the angle

Given an angle \( \theta = \frac{\pi}{4} \), find \( \tan(\theta) \).

Since the angle \( \theta \) is within the first quadrant and \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \), we have:

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

Therefore:

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

So, \( \tan(\frac{\pi}{4}) = 1 \).

To find the tangent of ( heta = frac{pi}{4} ), we use the fact that:

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

Since ( heta = frac{pi}{4} ), we know from the unit circle that:

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

Therefore,

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

Thus, the tangent of ( frac{pi}{4} ) is 1.

For ( heta = frac{pi}{4} ):

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

Since ( sin(frac{pi}{4}) = frac{sqrt{2}}{2} ) and ( cos(frac{pi}{4}) = frac{sqrt{2}}{2} ),

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

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