Find the Cosine of $45^circ$

To find the cosine of $45^\circ$, we use the unit circle. On the unit circle, the coordinates of the point where the terminal side of the $45^\circ$ angle intersects the circle are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$. The cosine of an angle is equal to the x-coordinate of this point.

Therefore,

$\cos(45^\circ) = \frac{\sqrt{2}}{2}$

Using the unit circle, the cosine of $45^circ$ is found by identifying the x-coordinate of the point where the terminal side of the angle intersects the circle. For $45^circ$, this point is $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.

Thus, the cosine is:

$cos(45^circ) = frac{sqrt{2}}{2}$

On the unit circle, the point for $45^circ$ is $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$. Therefore,

$cos(45^circ) = frac{sqrt{2}}{2}$

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