Answer
$=-\frac{\sqrt{6}+\sqrt{2}}{4}$
Work Step by Step
$\cos(195^\circ)$
$=\cos(225^\circ-30^\circ)$
Use the subtraction formula for cosine on page 545:
$=\cos(225^\circ)\cos(30^\circ)+\sin(225^\circ)\sin(30^\circ)$
Simplify (and remember that cosine and sine are both negative in the third quadrant):
$=-\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}+(\frac{-\sqrt{2}}{2})*\frac{1}{2}$
$=-\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{4}$
$=-\frac{\sqrt{6}+\sqrt{2}}{4}$
