Answer
$\frac{1}{2}$
Work Step by Step
Convert the angle measure to degrees to obtain:
$=\frac{5\pi}{6} \cdot \frac{180^o}{\pi} = 5(30^o)=150^0$
Thus,
$\sin{(\frac{5\pi}{6})}
\\= \sin{150^o}$
150 degrees is in Quadrant II so :
(i) its reference angle is $180^o-150^o=30^o$
(ii) its sine value is positive
From Section 2.1 (page 50) , we learned that:
$\sin{30^o} = \frac{1}{2}$
This means that:
$\sin{150^o} = \sin{30^o} = \frac{1}{2}$.
