Find the value of $cos(frac{pi}{4})$

To find the value of $\cos(\frac{\pi}{4})$, we must understand the unit circle. The angle $\frac{\pi}{4}$, or 45 degrees, is a special angle in the unit circle.

The coordinates of the point where the terminal side of the angle $\frac{\pi}{4}$ intersects the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$. The $x$-coordinate represents the cosine value.

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

To determine $cos(frac{pi}{4})$, we refer to the unit circle. The angle $frac{pi}{4}$ corresponds to 45 degrees.

In the unit circle, the coordinates at $frac{pi}{4}$ are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

The cosine of the angle is the $x$-coordinate, so we have:

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

Using the unit circle, the angle $frac{pi}{4}$ (45 degrees) gives coordinates $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

The cosine value is the $x$-coordinate:

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

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