What are the coordinates of the point on the unit circle where the angle is $frac{pi}{3}$?

To find the coordinates of the point on the unit circle at an angle of $\frac{\pi}{3}$ radians, we use the trigonometric functions cosine and sine.

For an angle $\theta = \frac{\pi}{3}$:

$ \cos \left( \frac{\pi}{3} \right) = \frac{1}{2} $

$ \sin \left( \frac{\pi}{3} \right) = \frac{\sqrt{3}}{2} $

Therefore, the coordinates are:

$( \cos \left( \frac{\pi}{3} \right), \sin \left( \frac{\pi}{3} \right) ) = \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $

The point on the unit circle corresponding to the angle $frac{pi}{3}$ can be found using the cosine and sine functions.

First, calculate the cosine of $frac{pi}{3}$:

$cos left( frac{pi}{3}
ight) = frac{1}{2}$

Next, calculate the sine of $frac{pi}{3}$:

$sin left( frac{pi}{3}
ight) = frac{sqrt{3}}{2}$

Thus, the coordinates of the point are:

$( frac{1}{2}, frac{sqrt{3}}{2} )$

For an angle of $frac{pi}{3}$,

$cos left( frac{pi}{3}
ight) = frac{1}{2}$

$sin left( frac{pi}{3}
ight) = frac{sqrt{3}}{2}$

Therefore, the coordinates are:

$( frac{1}{2}, frac{sqrt{3}}{2} )$

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