#### Answer

$\color{blue}{\cos{(\frac{3\pi}{4})}=-\dfrac{\sqrt2}{2}}$

#### Work Step by Step

Figure 13 on page 579 of this book shows that the unit circle point $(-\frac{\sqrt2}{2}, \frac{\sqrt2}{2})$ corresponds to the real number $\dfrac{3\pi}{4}$.
RECALL:
(i) $\cos{s} = x$
(ii) $\sin{s} = y$
(iii) $\tan{s}=\dfrac{y}{x}$
(iv) $\sec{s} =\dfrac{1}{x}$
(v) $\csc{s} = \dfrac{1}{y}$
(vi) $\cot{s} = \dfrac{x}{y}$
Use the coordinates of the unit circle point above and the formula in (i) above to obtain:
$\color{blue}{\cos{(\frac{3\pi}{4})}=-\frac{\sqrt2}{2}}$