Answer
$\frac{1}{2}$
Work Step by Step
RECALL:
$\sin{s} = y
\\\cos{s} = x
\\\tan{s} = \frac{y}{x}
\\\cot{s} = \frac{x}{y}
\\\sec{s} = \frac{1}{x}
\\\csc{s}=\frac{1}{y}$
(refer to Figure 11 on page 111 of the textbook)
The angle $\frac{7\pi}{6}$ intersect the unit circle at the point $(\frac{1}{2}, -\frac{\sqrt3}{2})$.
This point has:
$x= \frac{1}{2}$
$y=-\frac{\sqrt3}{2}$
Thus,
$\cos{\frac{5\pi}{3}} = \frac{1}{2}$