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

To find the coordinates of a point on the unit circle at an angle of $45^{\circ}$, we use the sine and cosine functions.

First, we convert the angle to radians:

$45^{\circ} = \frac{45 \pi}{180} = \frac{\pi}{4}$

Now, we find the sine and cosine of $\frac{\pi}{4}$:

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

$\sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$

Therefore, the coordinates of the point are:

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

To locate the coordinates of a point on the unit circle at $45^{circ}$, we use trigonometric functions.

Convert the angle to radians:

$45^{circ} = frac{pi}{4}$

Compute the cosine and sine values:

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

$sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

Thus, the point on the unit circle has coordinates:

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

To find the coordinates of a point on the unit circle at $45^{circ}$, we follow these steps:

Convert $45^{circ}$ to radians: $frac{pi}{4}$

Calculate:

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

$sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

The coordinates are:

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

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