Answer
$-\frac{\sqrt2}{2}$
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 , page 111 of the textbook)
This angle intersects the unit circle at the point $(-\frac{\sqrt2}{2}, \frac{\sqrt2}{2})$.
This point has:
$x= -\frac{\sqrt2}{2}$
$y=\frac{\sqrt2}{2}$
Thus,
$\cos{\frac{3\pi}{4}}=-\frac{\sqrt2}{2}$
