What is the cosine of an angle in the unit circle corresponding to $ frac{7pi}{6} $ radians?
Answer 1
Alex Thompson
To find the cosine of the angle $ \frac{7\pi}{6} $ in the unit circle, we first recognize that this angle is in the third quadrant. An angle in the third quadrant has a negative cosine value.
The reference angle for $ \frac{7\pi}{6} $ is $ \frac{\pi}{6} $.
Since the cosine of $ \frac{\pi}{6} $ is $ \frac{\sqrt{3}}{2} $, the cosine of $ \frac{7\pi}{6} $ is $ -\frac{\sqrt{3}}{2} $.
Therefore, $ \cos(\frac{7\pi}{6}) = -\frac{\sqrt{3}}{2} $.
Answer 2
James Taylor
To find $ cos(frac{7pi}{6}) $, note that the angle is in the third quadrant, where cosine values are negative.
The reference angle is $ frac{pi}{6} $, and $ cos(frac{pi}{6}) = frac{sqrt{3}}{2} $.
Thus, $ cos(frac{7pi}{6}) = -frac{sqrt{3}}{2} $.
Answer 3
Isabella Walker
$ cos(frac{7pi}{6}) $ is in the third quadrant with reference angle $ frac{pi}{6} $.
Thus, $ cos(frac{7pi}{6}) = -frac{sqrt{3}}{2} $.
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