What is the cosine of the angle at $ frac{2pi}{3} $ on the unit circle?
Answer 1
Amelia Mitchell
First, recognize that the angle $ \frac{2\pi}{3} $ is in the second quadrant.
In the unit circle, the cosine function is negative in the second quadrant.
The reference angle for $ \frac{2\pi}{3} $ is $ \pi – \frac{2\pi}{3} = \frac{\pi}{3} $.
We know that $ \cos\left( \frac{\pi}{3} \right) = \frac{1}{2} $.
Therefore, the cosine of $ \frac{2\pi}{3} $ is:
$\cos\left( \frac{2\pi}{3} \right) = -\cos\left( \frac{\pi}{3} \right) = -\frac{1}{2}$
Answer 2
John Anderson
We start by identifying the angle $ frac{2pi}{3} $ on the unit circle, which is in the second quadrant.
In this quadrant, the cosine value is negative.
The reference angle for $ frac{2pi}{3} $ is $ frac{pi}{3} $.
From trigonometric values, we know:
$cosleft( frac{pi}{3}
ight) = frac{1}{2}$
Thus, the cosine of $ frac{2pi}{3} $ is:
$cosleft( frac{2pi}{3}
ight) = -frac{1}{2}$
Answer 3
Michael Moore
The angle $ frac{2pi}{3} $ is in the second quadrant where cosine is negative.
Its reference angle is $ frac{pi}{3} $.
Thus, the cosine of $ frac{2pi}{3} $ is:
$cosleft( frac{2pi}{3}
ight) = -frac{1}{2}$
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