Find the coordinates of the point on the unit circle where the terminal side of the angle $ frac{5pi}{6} $ intersects the circle.

To find the coordinates of the point where the terminal side of the angle $ \frac{5\pi}{6} $ intersects the unit circle, we use the unit circle definition:

The coordinates are given by:

$ (\cos(\theta), \sin(\theta)) $

For $ \theta = \frac{5\pi}{6} $:

$ \cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2} $

$ \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} $

Thus, the coordinates are:

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

To determine the coordinates where $ frac{5pi}{6} $ intersects the unit circle, use:

$ (cos( heta), sin( heta)) $

For $ heta = frac{5pi}{6} $:

$ cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2} $

$ sinleft(frac{5pi}{6}
ight) = frac{1}{2} $

Hence, the coordinates are:

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

For the angle $ frac{5pi}{6} $ on the unit circle:

$ cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2} $

$ sinleft(frac{5pi}{6}
ight) = frac{1}{2} $

The coordinates are:

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

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