Find the values of $ sin frac{5pi}{6} $, $ cos frac{5pi}{6} $, and $ an frac{5pi}{6} $ using the unit circle.
Answer 1
Christopher Garcia
To find the values of $ \sin \frac{5\pi}{6} $, $ \cos \frac{5\pi}{6} $, and $ \tan \frac{5\pi}{6} $ using the unit circle, we first locate the angle $ \frac{5\pi}{6} $ on the unit circle.
The angle $ \frac{5\pi}{6} $ is in the second quadrant, where sine is positive and cosine is negative. The reference angle is $ \pi – \frac{5\pi}{6} = \frac{\pi}{6} $.
From the unit circle, we know:
$ \sin \frac{\pi}{6} = \frac{1}{2} $ and $ \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} $
Since we are in the second quadrant:
$ \sin \frac{5\pi}{6} = \frac{1}{2} $
$ \cos \frac{5\pi}{6} = -\frac{\sqrt{3}}{2} $
$ \tan \frac{5\pi}{6} = \frac{ \sin \frac{5\pi}{6} }{ \cos \frac{5\pi}{6} } = \frac{ \frac{1}{2} }{ -\frac{\sqrt{3}}{2} } = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3} $
Answer 2
Charlotte Davis
To find the values of $ sin frac{5pi}{6} $, $ cos frac{5pi}{6} $, and $ an frac{5pi}{6} $ using the unit circle, we locate the angle $ frac{5pi}{6} $ in the second quadrant. The reference angle is $ frac{pi}{6} $.
From the unit circle, we have:
$ sin frac{pi}{6} = frac{1}{2} $ and $ cos frac{pi}{6} = frac{sqrt{3}}{2} $
Therefore:
$ sin frac{5pi}{6} = frac{1}{2} $
$ cos frac{5pi}{6} = -frac{sqrt{3}}{2} $
$ an frac{5pi}{6} = -frac{sqrt{3}}{3} $
Answer 3
Lucas Brown
To find the values of $ sin frac{5pi}{6} $, $ cos frac{5pi}{6} $, and $ an frac{5pi}{6} $ using the unit circle, note that $ frac{5pi}{6} $ is in the second quadrant with a reference angle of $ frac{pi}{6} $.
Thus:
$ sin frac{5pi}{6} = frac{1}{2} $
$ cos frac{5pi}{6} = -frac{sqrt{3}}{2} $
$ an frac{5pi}{6} = -frac{sqrt{3}}{3} $
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