Determine the sine and cosine values of $ frac{5pi}{6} $
Answer 1
John Anderson
To determine the sine and cosine values of $ \frac{5\pi}{6} $, we refer to the unit circle.
The angle $ \frac{5\pi}{6} $ is located in the second quadrant.
In the second quadrant, sine is positive, and cosine is negative.
The reference angle for $ \frac{5\pi}{6} $ is $ \frac{\pi}{6} $.
Therefore:
$ \sin(\frac{5\pi}{6}) = \sin(\pi – \frac{\pi}{6}) = \sin(\frac{\pi}{6}) = \frac{1}{2} $
$ \cos(\frac{5\pi}{6}) = \cos(\pi – \frac{\pi}{6}) = -\cos(\frac{\pi}{6}) = -\frac{\sqrt{3}}{2} $
Answer 2
James Taylor
To find the sine and cosine of $ frac{5pi}{6} $, we use the unit circle:
The angle $ frac{5pi}{6} $ is in the second quadrant.
Sine is positive and cosine is negative in the second quadrant.
The reference angle is $ frac{pi}{6} $.
Therefore,
$ sin(frac{5pi}{6}) = frac{1}{2} $
$ cos(frac{5pi}{6}) = -frac{sqrt{3}}{2} $
Answer 3
Abigail Nelson
Using the unit circle for $ frac{5pi}{6} $:
$ sin(frac{5pi}{6}) = frac{1}{2} $
$ cos(frac{5pi}{6}) = -frac{sqrt{3}}{2} $
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