Answer
$\sin{\frac{3\pi}{4}} = \frac{\sqrt2}{2}$
Work Step by Step
Recall:
(1) An angle and its reference angle either have the same trigonometric function values or differ only in signs.
(2) $\frac{\pi}{4}$ is a special angle whose sine value is known to be $\frac{\sqrt2}{2}$.
Note that the reference angle of $\frac{3\pi}{4}$ is $\frac{\pi}{4}$.
However, since $\frac{3\pi}{4}$ is in Quadrant II, then its sine value is also positive.
Therefore,
$\sin{\frac{3\pi}{4}} = \frac{\sqrt2}{2}$
