Find the coordinates on the Unit Circle

To determine the coordinates on the unit circle corresponding to an angle of $ \frac{5\pi}{6} $, we use the trigonometric functions sine and cosine.

The cosine of $ \frac{5\pi}{6} $ corresponds to the x-coordinate, and the sine of $ \frac{5\pi}{6} $ corresponds to the y-coordinate.

Calculating these values:

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

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

So, the coordinates are:

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

Given an angle of $ frac{5pi}{6} $ on the unit circle, the x-coordinate is found using the cosine function, and the y-coordinate is found using the sine function.

For $ frac{5pi}{6} $, we calculate:

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

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

Thus, the coordinates are:

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

The coordinates for $ frac{5pi}{6} $ on the unit circle are:

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

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

Coordinates:

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

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