Determine the coordinates of the point where the angle $ heta = frac{pi}{3} $ on the unit circle

First, recall that the unit circle has a radius of 1. For the angle $ \theta = \frac{\pi}{3} $, we use the definitions of sine and cosine:

$ x = \cos(\theta) $

$ y = \sin(\theta) $

When $ \theta = \frac{\pi}{3} $, we have:

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

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

Therefore, the coordinates of the point are:

$ \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $

For the angle $ heta = frac{pi}{3} $ on the unit circle, use the cosine and sine functions:

$ x = cosleft(frac{pi}{3}
ight) = frac{1}{2} $

$ y = sinleft(frac{pi}{3}
ight) = frac{sqrt{3}}{2} $

Thus, the coordinates are:

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

For $ heta = frac{pi}{3} $:

$ x = cosleft(frac{pi}{3}
ight) = frac{1}{2} $

$ y = sinleft(frac{pi}{3}
ight) = frac{sqrt{3}}{2} $

Coordinates:

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

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