Fill in the unit circle with the corresponding coordinates for the angle of $45^circ$.

To find the coordinates of the angle $45^\circ$ on the unit circle, we use the fact that at $45^\circ$, both the $x$-coordinate and $y$-coordinate are equal.

In the unit circle, this coordinate is found by:

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

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

Thus, the coordinates for the angle $45^\circ$ are:

$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $

The angle $45^circ$ is in the first quadrant of the unit circle.

Since $cos(45^circ) = sin(45^circ)$ and is positive in the first quadrant:

We get:

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

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

Thus, the coordinates for the angle $45^circ$ are:

$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $

For the angle $45^circ$, the coordinates are:

$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $

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