Find the coordinates of the point on the unit circle corresponding to an angle of $frac{pi}{3}$ radians.

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

The coordinates are given by: $ (\cos(\frac{\pi}{3}), \sin(\frac{\pi}{3})) $

First, calculate the cosine: $ \cos(\frac{\pi}{3}) = \frac{1}{2} $

Next, calculate the sine: $ \sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2} $

Therefore, the coordinates are: $ \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $

To determine the coordinates on the unit circle for an angle of $frac{pi}{3}$ radians, we will use trigonometric functions.

The coordinates can be found using: $ (cos(frac{pi}{3}), sin(frac{pi}{3})) $

For the cosine component: $ cos(frac{pi}{3}) = frac{1}{2} $

For the sine component: $ sin(frac{pi}{3}) = frac{sqrt{3}}{2} $

So, the point is: $ left( frac{1}{2}, frac{sqrt{3}}{2}
ight) $

To find the coordinates at an angle of $frac{pi}{3}$ radians on the unit circle, we use the formulas:

$ (cos(frac{pi}{3}), sin(frac{pi}{3})) $

Calculating these values gives:

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

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

Therefore, the coordinates are: $ left( frac{1}{2}, frac{sqrt{3}}{2}
ight) $

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