Find the value of $ tan(frac{pi}{4}) $ using the unit circle.

To find the value of $ tan(\frac{\pi}{4}) $ using the unit circle, we need to consider the coordinates of the point on the unit circle at the angle $ \frac{\pi}{4} $. The coordinates of this point are $ (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) $.

The tangent function is defined as the ratio of the y-coordinate to the x-coordinate:

$ tan(\theta) = \frac{y}{x} $

So,

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

Therefore, the value of $ tan(\frac{\pi}{4}) $ is 1.

Using the unit circle, the point at $ frac{pi}{4} $ radians is $ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $.

Recall that $ tan( heta) = frac{y}{x} $. Hence,

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

After simplifying, we get:

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

Thus, the value of $ tan(frac{pi}{4}) $ is 1.

The coordinates on the unit circle at $ frac{pi}{4} $ are $ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $. Since $ tan( heta) = frac{y}{x} $:

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

Hence, $ tan(frac{pi}{4}) = 1 $.

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