Answer
$s = \displaystyle \frac{5\pi}{6}$
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 characteristic point with the y-coordinate (sine) of $\displaystyle \frac{1}{2}.$
We find the point$: (-\displaystyle \frac{\sqrt{3}}{2}, \frac{1}{2}) $assigned to $150^{o}$, or $\displaystyle \frac{5\pi}{6}$ rad.
$\displaystyle \sin\frac{5\pi}{6}=\frac{1}{2},$
$s = \displaystyle \frac{5\pi}{6}$
