Find the value of $ arcsin(sqrt{3}/2) $ based on the unit circle
Answer 1
Isabella Walker
To find the value of $ \arcsin(\sqrt{3}/2) $, we need to locate where $ \sin(x) = \sqrt{3}/2 $ on the unit circle.
On the unit circle, $ \sin(x) = \sqrt{3}/2 $ at the angles:
$ x = \frac{\pi}{3} $
and
$ x = \frac{2\pi}{3} $
So,
$ \arcsin(\sqrt{3}/2) = \frac{\pi}{3} $
in the primary range of arcsin, which is $ [ -\frac{\pi}{2}, \frac{\pi}{2} ] $.
Answer 2
Joseph Robinson
To determine $ arcsin(sqrt{3}/2) $, we look for the angle $ x $ where $ sin(x) = sqrt{3}/2 $ within the interval $ [-frac{pi}{2}, frac{pi}{2}] $.
The value of $ sin(x) = sqrt{3}/2 $ occurs at:
$ x = frac{pi}{3} $
Thus,
$ arcsin(sqrt{3}/2) = frac{pi}{3} $
Answer 3
John Anderson
To find $ arcsin(sqrt{3}/2) $, locate where $ sin(x) = sqrt{3}/2 $ on the unit circle, which is:
$ x = frac{pi}{3} $
Therefore,
$ arcsin(sqrt{3}/2) = frac{pi}{3} $
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