Calculate the exact value of $ cos(frac{5pi}{6}) $ using the unit circle

We must first determine the reference angle for $ \frac{5\pi}{6} $. This angle is in the second quadrant.

The reference angle for $ \frac{5\pi}{6} $ is $ \pi – \frac{5\pi}{6} = \frac{\pi}{6} $.

In the second quadrant, the cosine function is negative. Thus,

$ \cos(\frac{5\pi}{6}) = -\cos(\frac{\pi}{6}) $

We know that $ \cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2} $, therefore,

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

To find the value of $ cos(frac{5pi}{6}) $, we first identify the corresponding reference angle.

The reference angle in the second quadrant is $ frac{pi}{6} $ since $ pi – frac{5pi}{6} = frac{pi}{6} $.

Considering the unit circle, we know $ cos $ is negative in the second quadrant:

$ cos(frac{5pi}{6}) = -cos(frac{pi}{6}) $

From trigonometric values, $ cos(frac{pi}{6}) = frac{sqrt{3}}{2} $, and hence,

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

In the second quadrant, $ frac{5pi}{6} $ has a reference angle of $ frac{pi}{6} $.

Using the unit circle, $ cos $ is negative in this quadrant:

$ cos(frac{5pi}{6}) = -cos(frac{pi}{6}) $

With $ cos(frac{pi}{6}) = frac{sqrt{3}}{2} $, we get,

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

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