Determine the coordinates of the point where the terminal side of an angle of $ frac{5pi}{3} $ radians intersects the unit circle, and identify its quadrant

The angle $ \frac{5\pi}{3} $ radians is equivalent to 300 degrees (since $ \frac{5\pi}{3} \times \frac{180}{\pi} = 300 $ degrees).

This angle places the terminal side in the fourth quadrant.

In the fourth quadrant, the coordinates on the unit circle corresponding to an angle of 300 degrees are:

$ ( \cos(300\degree), \sin(300\degree) ) $

Since $ \cos(300\degree) = \cos(-60\degree) = \frac{1}{2} $ and $ \sin(300\degree) = \sin(-60\degree) = -\frac{\sqrt{3}}{2} $, the coordinates are:

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

Thus, the terminal side intersects the unit circle at $ \left( \frac{1}{2}, -\frac{\sqrt{3}}{2} \right) $ in the fourth quadrant.

The angle $ frac{5pi}{3} $ radians is equivalent to 300 degrees. This places the terminal side in the fourth quadrant.

The coordinates on the unit circle for an angle of 300 degrees are: $ ( cos(300degree), sin(300degree) ) $

Since $ cos(300degree) = frac{1}{2} $ and $ sin(300degree) = -frac{sqrt{3}}{2} $, the coordinates are:

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

The terminal side intersects the unit circle at $ left( frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ in the fourth quadrant.

The angle $ frac{5pi}{3} $ radians is equivalent to 300 degrees, placing it in the fourth quadrant.

The coordinates for 300 degrees on the unit circle are:

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

The terminal side intersects the unit circle at $ left( frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ in the fourth quadrant.

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