”Determine

First, consider the unit circle where the cosine value is $\frac{-1}{2}$. In the interval $[\pi, 2\pi]$, the angle where the cosine is $\frac{-1}{2}$ is $\frac{4\pi}{3}$.

To find the corresponding sine value:

$\sin\left(\frac{4\pi}{3}\right) = -\frac{\sqrt{3}}{2}$

To find the tangent value:

$\tan\left(\frac{4\pi}{3}\right) = \frac{\sin\left(\frac{4\pi}{3}\right)}{\cos\left(\frac{4\pi}{3}\right)} = \frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}} = \sqrt{3}$

Therefore, the coordinates on the unit circle are:

$\left(\cos\left(\frac{4\pi}{3}\right), \sin\left(\frac{4\pi}{3}\right)\right) = \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$

We start by identifying the angle in the unit circle where the cosine value is $frac{-1}{2}$. Within the interval $[pi, 2pi]$, the angle is $frac{4pi}{3}$.

Next, we find the sine of $frac{4pi}{3}$:

$sinleft(frac{4pi}{3}
ight) = -frac{sqrt{3}}{2}$

Then, to find the tangent:

$ anleft(frac{4pi}{3}
ight) = frac{sinleft(frac{4pi}{3}
ight)}{cosleft(frac{4pi}{3}
ight)} = sqrt{3}$

The coordinates on the unit circle at this angle are:

$left(cosleft(frac{4pi}{3}
ight), sinleft(frac{4pi}{3}
ight)
ight) = left(-frac{1}{2}, -frac{sqrt{3}}{2}
ight)$

The angle in the unit circle where the cosine is $frac{-1}{2}$ in the interval $[pi, 2pi]$ is $frac{4pi}{3}$.

The sine value:

$sinleft(frac{4pi}{3}
ight) = -frac{sqrt{3}}{2}$

The tangent value:

$ anleft(frac{4pi}{3}
ight) = sqrt{3}$

Coordinates on the unit circle:

$left(-frac{1}{2}, -frac{sqrt{3}}{2}
ight)$

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