Answer
$s = \displaystyle \frac{2\pi}{3}$ or $\displaystyle \frac{4\pi}{3}$
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 $[0,2\pi)$, (the unit circle), we search for
points (x,y), such that $x=-\displaystyle \frac{1}{2}$
$(\cos s=x$, negative in quadrants II and III$)$
We find points$:$
$(-\displaystyle \frac{1}{2},\displaystyle \frac{\sqrt{3}}{2})\quad $in quadrant II,
assigned to $120^{o}$, or $\displaystyle \frac{2\pi}{3}$ rad.
and
$(-\displaystyle \frac{1}{2},-\displaystyle \frac{\sqrt{3}}{2}) \quad $in quadrant III,
assigned to $240^{o}$, or $\displaystyle \frac{4\pi}{3}$ rad.
$s = \displaystyle \frac{2\pi}{3}$ or $\displaystyle \frac{4\pi}{3}$
