Answer
$-1$
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 $\frac{3\pi}{4}$ 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,
$\tan{\frac{3\pi}{4}} = \frac{y}{x}=\dfrac{\frac{\sqrt2}{2}}{-\frac{\sqrt2}{2}}=-1$
