Find the sine and cosine of $ frac{7pi}{6} $ on the unit circle.
Answer 1
Michael Moore
To find the sine and cosine of $ \frac{7\pi}{6} $ on the unit circle, we first determine the reference angle. The reference angle for $ \frac{7\pi}{6} $ is $ \frac{\pi}{6} $.
The sine and cosine of $ \frac{7\pi}{6} $ correspond to the sine and cosine of $ \frac{\pi}{6} $ but with signs corresponding to the third quadrant.
From the unit circle, we know:
$ \sin \left( \frac{\pi}{6} \right) = \frac{1}{2} $
$ \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} $
Since $ \frac{7\pi}{6} $ is in the third quadrant, where both sine and cosine are negative, we get:
$ \sin \left( \frac{7\pi}{6} \right) = -\frac{1}{2} $
$ \cos \left( \frac{7\pi}{6} \right) = -\frac{\sqrt{3}}{2} $
Answer 2
Benjamin Clark
We need to find the sine and cosine of $ frac{7pi}{6} $ on the unit circle. The reference angle for $ frac{7pi}{6} $ is $ frac{pi}{6} $.
The sine and cosine of $ frac{7pi}{6} $ are the same as those of $ frac{pi}{6} $ but with signs of the third quadrant, where both are negative:
$ sin left( frac{7pi}{6}
ight) = -frac{1}{2} $
$ cos left( frac{7pi}{6}
ight) = -frac{sqrt{3}}{2} $
Answer 3
Henry Green
The reference angle for $ frac{7pi}{6} $ is $ frac{pi}{6} $.
In the third quadrant, both sine and cosine are negative:
$ sin left( frac{7pi}{6}
ight) = -frac{1}{2} $
$ cos left( frac{7pi}{6}
ight) = -frac{sqrt{3}}{2} $
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