Find the values of $ arcsin( frac{1}{2} ) $ using the unit circle

To find the values of $ \arcsin( \frac{1}{2} ) $ using the unit circle, we look for the angles $ \theta $ whose sine value is $ \frac{1}{2} $.

On the unit circle, the sine value is the y-coordinate. The angles with a y-coordinate of $ \frac{1}{2} $ are:

$ \theta = \frac{\pi}{6} $

or

$ \theta = \frac{5\pi}{6} $

So, the values of $ \arcsin( \frac{1}{2} ) $ are:

$ \frac{\pi}{6} $ and $ \frac{5\pi}{6} $

Using the unit circle, the angles with sine $ frac{1}{2} $ are:

$ heta = frac{pi}{6} $

and

$ heta = frac{5pi}{6} $

Therefore, $ arcsin( frac{1}{2} ) $ gives:

$ frac{pi}{6} $ and $ frac{5pi}{6} $

For $ arcsin( frac{1}{2} ) $:

$ frac{pi}{6} $

and

$ frac{5pi}{6} $

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