$ ext{Find the angle } heta ext{ in the unit circle where } cos( heta) = 0.5$

$\text{Given } \cos(\theta) = 0.5$

$\text{We know that } \cos(\theta) = 0.5 \text{ at } \theta = \frac{\pi}{3} \text{ and } \theta = -\frac{\pi}{3} \text{ (or equivalently } \theta = 2\pi – \frac{\pi}{3} = \frac{5\pi}{3} \text{)}$

$\text{Therefore, the angles } \theta \text{ in radians where } \cos(\theta) = 0.5 \text{ are } \theta = \frac{\pi}{3} \text{ and } \theta = \frac{5\pi}{3}.$

$ ext{We know that } cos( heta) ext{ is positive in the first and fourth quadrants.}$

$ ext{In the first quadrant, } cos( heta) = 0.5 ext{ corresponds to } heta = frac{pi}{3}.$

$ ext{In the fourth quadrant, } cos( heta) = 0.5 ext{ corresponds to } heta = 2pi – frac{pi}{3} = frac{5pi}{3}.$

$ ext{Thus, the angles where } cos( heta) = 0.5 ext{ are } heta = frac{pi}{3} ext{ and } heta = frac{5pi}{3}.$

$cos( heta) = 0.5$

$ heta = frac{pi}{3} ext{ and } frac{5pi}{3}.$

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