Convert the angle to degrees:

$\displaystyle\frac{{{3}\pi}}{{4}}=\frac{{{3}\pi}}{{4}}\cdot\frac{{{180}}^{\circ}}{\pi}=\frac{{{{540}}^{\circ}}}{{4}}={{135}}^{\circ}\usepackage{cmbright}\Huge\$

This is in the second quadrant and its reference angle is $\displaystyle{{45}}^{\circ}\usepackage{cmbright}\Huge\$ . It intersects the unit circle at the point $\displaystyle{\left(-\frac{\sqrt{{2}}}{{2}},\frac{\sqrt{{2}}}{{2}}\right)}\usepackage{cmbright}\Huge\$ . The value of cosine is the x-coordinate:

$\displaystyle{\cos{{\left(\frac{{{3}\pi}}{{4}}\right)}}}=-\frac{\sqrt{{2}}}{{2}}\usepackage{cmbright}\Huge\$