Find the coordinates of the point on the unit circle at 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 formula for the coordinates on the unit circle: $ ( \cos \theta, \sin \theta ) $.

Here, $ \theta = \frac{\pi}{3} $.

So, we need to find $ \cos \frac{\pi}{3} $ and $ \sin \frac{\pi}{3} $.

From trigonometric values, we know that:

$ \cos \frac{\pi}{3} = \frac{1}{2} $

$ \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} $

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

To determine the coordinates for the angle $ frac{pi}{3} $ radians on the unit circle, we use $ ( cos heta, sin heta ) $ where $ heta = frac{pi}{3} $.

The values are:

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

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

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

Using $ ( cos heta, sin heta ) $ for $ heta = frac{pi}{3} $, we get:

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

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

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

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