Answer
$s = \displaystyle \frac{4\pi}{3}$
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 $[\pi,\displaystyle \frac{3\pi}{2}]$, (quadrant III), we search for
a point (x,y) on the unit circle, such that $\displaystyle \frac{y}{x}=\sqrt{3}$
We find the point$:$
$(-\displaystyle \frac{\sqrt{3}}{2},-\frac{1}{2}) $ assigned to $240^{o}$, or $\displaystyle \frac{4\pi}{3}$ rad.
$\displaystyle \tan\frac{4\pi}{3}=\frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=\sqrt{3},$
$s = \displaystyle \frac{4\pi}{3}$