Determine the coordinates of a point on the unit circle at an angle of $ frac{11pi}{6} $
Answer 1
John Anderson
To determine the coordinates of a point on the unit circle at an angle of $ \frac{11\pi}{6} $, we use the unit circle properties.
The coordinates can be found using the cosine and sine of the angle:
$ x = \cos \left( \frac{11\pi}{6} \right) $
$ y = \sin \left( \frac{11\pi}{6} \right) $
Since $ \frac{11\pi}{6} $ is in the fourth quadrant, we know:
$ \cos \left( \frac{11\pi}{6} \right) = \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} $
$ \sin \left( \frac{11\pi}{6} \right) = -\sin \left( \frac{\pi}{6} \right) = -\frac{1}{2} $
So the coordinates are:
$ \left( \frac{\sqrt{3}}{2}, -\frac{1}{2} \right) $
Answer 2
Ava Martin
To determine the coordinates of a point on the unit circle at an angle of $ frac{11pi}{6} $, we use the following trigonometric identities:
$ x = cos left( frac{11pi}{6}
ight) $
$ y = sin left( frac{11pi}{6}
ight) $
Given that $ frac{11pi}{6} $ is in the fourth quadrant:
$ cos left( frac{11pi}{6}
ight) = frac{sqrt{3}}{2} $
$ sin left( frac{11pi}{6}
ight) = -frac{1}{2} $
The coordinates are:
$ left( frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
Answer 3
Henry Green
To find the coordinates at $ frac{11pi}{6} $:
$ x = cos left( frac{11pi}{6}
ight) = frac{sqrt{3}}{2} $
$ y = sin left( frac{11pi}{6}
ight) = -frac{1}{2} $
The coordinates are:
$ left( frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
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