Answer
$-\dfrac{\sqrt{2}}{2}$
Work Step by Step
RECALL:
(1)The reference angle of a given angle is equal to the smallest acute angle that the terminal side makes with the x-axis.
(2) Based on the location of the terminal side of an angle $\theta$, the reference angle can be found using the formula:
(i) Quadrant I: $\theta$
(ii) Quadrant II: $\pi-\theta$
(iii) Quadrant III: $\theta-\pi$
(iv) Quadrant IV: $2\pi-\theta$
The given angle is in Quadrant II so its reference angle is:
$=\pi - \dfrac{3\pi}{4}
\\=\dfrac{\pi}{4}$
The value of cosine in Quadrant II is negative.
Thus,
$\cos{\frac{3\pi}{4}} = -\cos{\frac{\pi}{4}}$
$\dfrac{\pi}{4}$ is a special angle whose cosine value is $\dfrac{\sqrt{2}}{2}$.
Thus,
$\cos{\dfrac{3\pi}{4}}=-\cos{\dfrac{\pi}{4}}=-\dfrac{\sqrt{2}}{2}$