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To find the angle $ \theta $ in radians where $ \cos(\theta) = -\frac{1}{2} $ and $ 0 \leq \theta < 2\pi $, we look for the points on the unit circle where the x-coordinate is -1/2.

These points correspond to angles in the second and third quadrants.

In the second quadrant, the angle is:

$ \theta = \pi – \frac{\pi}{3} = \frac{2\pi}{3} $

In the third quadrant, the angle is:

$ \theta = \pi + \frac{\pi}{3} = \frac{4\pi}{3} $

Therefore, the angles are:

$ \theta = \frac{2\pi}{3} \text{ and } \frac{4\pi}{3} $

To find $ heta $ where $ cos( heta) = -frac{1}{2} $:

In the second quadrant:

$ heta = frac{2pi}{3} $

In the third quadrant:

$ heta = frac{4pi}{3} $

For $ cos( heta) = -frac{1}{2} $, $ heta = frac{2pi}{3} $ or $ frac{4pi}{3} $

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