Calculate the exact values of $ sin $ and $ cos $ at $ heta = frac{5pi}{6} $

To find the exact values of $ \sin $ and $ \cos $ at $ \theta = \frac{5\pi}{6} $, we use the unit circle.

First, find the reference angle:

$ \theta_{ref} = \pi – \frac{5\pi}{6} = \frac{\pi}{6} $

Using the reference angle $ \frac{\pi}{6} $, we know the exact values for sine and cosine are:

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

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

Since $ \theta = \frac{5\pi}{6} $ is in the second quadrant, sine is positive, and cosine is negative.

Therefore:

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

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

To find the exact values of $ sin $ and $ cos $ at $ heta = frac{5pi}{6} $, use the unit circle.

The reference angle is:

$ heta_{ref} = pi – frac{5pi}{6} = frac{pi}{6} $

From $ frac{pi}{6} $, we get:

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

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

In the second quadrant, sine is positive, cosine is negative:

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

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

To find the exact values of $ sin $ and $ cos $ at $ heta = frac{5pi}{6} $, use the unit circle.

The reference angle is $ frac{pi}{6} $:

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

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

In the second quadrant:

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

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

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