Answer
$s = \displaystyle \frac{2\pi}{3}$
Work Step by Step
For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
Use Figure 13 on page 111.
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In the interval $[\displaystyle \frac{\pi}{2},\pi]$, (quadrant II), we search for
a point with the $x$-coordinate (cosine) of $-\displaystyle \frac{1}{2}.$
on the unit circle.
We find the point$:$
$(-\displaystyle \frac{1}{2},\frac{\sqrt{3}}{2}) $assigned to $120^{o}$, or $\displaystyle \frac{2\pi}{3}$ rad.
$\displaystyle \cos\frac{2\pi}{3}=-\frac{1}{2},$
$s = \displaystyle \frac{2\pi}{3}$
