Find the angle $ heta $ in the unit circle such that $ cos( heta) = -frac{1}{2} $.
Answer 1
Lily Perez
We know that $ \cos(\theta) = -\frac{1}{2} $.
This value of cosine corresponds to two angles in the unit circle, which are in the second and third quadrants.
In the second quadrant, the reference angle is $ \theta = \pi – \frac{\pi}{3} = \frac{2\pi}{3} $.
In the third quadrant, the reference angle is $ \theta = \pi + \frac{\pi}{3} = \frac{4\pi}{3} $.
Therefore, $ \theta = \frac{2\pi}{3} $ or $ \theta = \frac{4\pi}{3} $.
Answer 2
Matthew Carter
Given $ cos( heta) = -frac{1}{2} $, we look for angles where the cosine value is $ -frac{1}{2} $.
By reference to the unit circle, we know that:
In the second quadrant, the angle is $ heta = pi – frac{pi}{3} = frac{2pi}{3} $.
In the third quadrant, the angle is $ heta = pi + frac{pi}{3} = frac{4pi}{3} $.
Thus, the angles that satisfy $ cos( heta) = -frac{1}{2} $ are $ heta = frac{2pi}{3} $ and $ heta = frac{4pi}{3} $.
Answer 3
Emma Johnson
To find $ heta $ such that $ cos( heta) = -frac{1}{2} $, we check the unit circle.
The angles are $ heta = frac{2pi}{3} $ and $ heta = frac{4pi}{3} $.
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