Find the angle $ heta $ in radians for a point on the unit circle that satisfies given conditions

Given a point $ P $ on the unit circle, where the coordinates of $ P $ are $ ( \cos(\theta), \sin(\theta) ) $.

If the coordinates of $ P $ are given as $ \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $, we need to determine the angle $ \theta $.

On the unit circle, these coordinates correspond to:

$ \cos(\theta) = \frac{1}{2} \quad \text{and} \quad \sin(\theta) = \frac{\sqrt{3}}{2} $

From the unit circle, we know that:

$ \theta = \frac{\pi}{3} $

Since the angle $ \theta $ can also be in the second quadrant, we have:

$ \theta = \frac{5\pi}{3} $

Given a point $ P $ on the unit circle, with coordinates $ ( cos( heta), sin( heta) ) $.

If the coordinates of $ P $ are $ left( frac{1}{2}, frac{sqrt{3}}{2}
ight) $, we need to find $ heta $.

These coordinates correspond to:

$ cos( heta) = frac{1}{2} ext{ and } sin( heta) = frac{sqrt{3}}{2} $

Thus:

$ heta = frac{pi}{3} $

Or:

$ heta = frac{5pi}{3} $

Given a point $ P $ on the unit circle with coordinates $ left( frac{1}{2}, frac{sqrt{3}}{2}
ight) $, find $ heta $.

These coordinates give:

$ heta = frac{pi}{3} ext{ or } frac{5pi}{3} $

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