$ ext{Find the coordinates of point } P ext{ on the unit circle at an angle of } 45^circ $

To find the coordinates of point P on the unit circle at an angle of 45 degrees, we use the fact that the unit circle has a radius of 1 and that the coordinates correspond to the cosine and sine of the angle.

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

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

Therefore, the coordinates of point P are:

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

Given an angle of 45 degrees on the unit circle, we use trigonometric identities to find the corresponding coordinates.

The unit circle has a radius of 1, so the coordinates are given by:

$ x = cos(45^circ) $

$ y = sin(45^circ) $

Using known values:

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

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

Thus, the coordinates of the point are:

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

The coordinates of a point on the unit circle at 45 degrees can be found using trigonometric functions:

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

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

Thus, the coordinates are:

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

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