Answer
$\color{blue}{\tan{(\frac{3\pi}{4})}=-1}$
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) $\tan{s}=\dfrac{y}{x}$
Use the coordinates of the unit circle point above and the formula in (iii) above to obtain:
$\color{blue}{\tan{(\frac{3\pi}{4})}=\frac{\frac{\sqrt2}{2}}{-\frac{\sqrt2}{2}}=-1}$
