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)
A negative angle measure means the terminal side of the angle will move clockwise from the positive x-axis.
Thus, from the positive x-axis, moving the terminal side $\frac{4\pi}{3}$ radians clockwise ends at $\frac{2\pi}{3}$.
The angle $\frac{2\pi}{3}$ intersects the unit circle at the point $(-\frac{1}{2}, \frac{\sqrt3}{2})$.
This point has:
$x= -\frac{1}{2}$
$y=\frac{\sqrt3}{2}$
Thus,
$\cos{(-\frac{4\pi}{3}}
\\= \cos{\frac{2\pi}{3}}
\\=-\frac{1}{2}$
