Determine the sine and cosine values for an angle of $ frac{5pi}{6} $ radians on the unit circle
Answer 1
Emily Hall
To find the sine and cosine of $ \frac{5\pi}{6} $ on the unit circle, we use the reference angle and the fact that it lies in Quadrant II:
The reference angle for $ \frac{5\pi}{6} $ is $ \pi – \frac{5\pi}{6} = \frac{\pi}{6} $.
In Quadrant II, sine is positive and cosine is negative. Therefore:
$ \sin\left( \frac{5\pi}{6} \right) = \sin\left( \frac{\pi}{6} \right) = \frac{1}{2} $
$ \cos\left( \frac{5\pi}{6} \right) = -\cos\left( \frac{\pi}{6} \right) = -\frac{\sqrt{3}}{2} $
Answer 2
Ava Martin
For the angle $ frac{5pi}{6} $ in Quadrant II:
The reference angle is $ frac{pi}{6} $.
So, $ sinleft( frac{5pi}{6}
ight) = frac{1}{2} $ and $ cosleft( frac{5pi}{6}
ight) = -frac{sqrt{3}}{2} $
Answer 3
Joseph Robinson
$ sinleft( frac{5pi}{6}
ight) = frac{1}{2} $
$ cosleft( frac{5pi}{6}
ight) = -frac{sqrt{3}}{2} $
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