Find the value of $ arcsin(x) $ for $ x = sqrt{3}/2 $ on the unit circle
Answer 1
Joseph Robinson
To find the value of $ \arcsin(x) $ for $ x = \sqrt{3}/2 $ on the unit circle, we need to determine the angle $ \theta $ such that $ \sin(\theta) = \sqrt{3}/2 $ and $ \theta $ lies in the range $ [-\frac{\pi}{2}, \frac{\pi}{2}] $.
The angle $ \theta $ corresponding to $ \sin(\theta) = \sqrt{3}/2 $ is $ \frac{\pi}{3} $.
Hence, $ \arcsin(\sqrt{3}/2) = \frac{\pi}{3} $.
Answer 2
Charlotte Davis
For $ x = sqrt{3}/2 $, we need to find the angle $ heta $ such that $ sin( heta) = sqrt{3}/2 $ within $ [-frac{pi}{2}, frac{pi}{2}] $.
The value is $ heta = frac{pi}{3} $.
Therefore, $ arcsin(sqrt{3}/2) = frac{pi}{3} $.
Answer 3
James Taylor
For $ x = sqrt{3}/2 $, $ arcsin(sqrt{3}/2) $ is $ frac{pi}{3} $.
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