Find the sine, cosine, and tangent values for the angle $ heta = frac{pi}{4}$ on the unit circle.

To find the sine, cosine, and tangent values for $\theta = \frac{\pi}{4}$, we use the unit circle properties.

For $\theta = \frac{\pi}{4}$:

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

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

$\tan\left( \frac{\pi}{4} \right) = 1$

First, determine the coordinates of the point on the unit circle corresponding to $ heta = frac{pi}{4}$.

The coordinates are $left( cosleft( frac{pi}{4}
ight), sinleft( frac{pi}{4}
ight)
ight) = left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

Therefore:

$sinleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$cosleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$ anleft( frac{pi}{4}
ight) = frac{sinleft( frac{pi}{4}
ight)}{cosleft( frac{pi}{4}
ight)} = 1$

Given $ heta = frac{pi}{4}$:

$sinleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$cosleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$ anleft( frac{pi}{4}
ight) = 1$

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