Find the coordinates of a point on the unit circle at $45^{circ}$.

The unit circle is a circle with a radius of 1 centered at the origin. To find the coordinates of a point at $45^{\circ}$, we use the trigonometric functions sine and cosine.

For $\theta = 45^{\circ}$:

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

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

Therefore, the coordinates of the point are:

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

The unit circle has a radius of 1. For an angle of $45^{circ}$, the coordinates of the point can be determined by the cosine and sine functions.

Using $ heta = 45^{circ}$:

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

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

Thus, the point on the unit circle at $45^{circ}$ is:

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

For an angle of $45^{circ}$ on the unit circle:

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

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

The coordinates are:

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

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