Find the Exact Value cos(135)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

The exact value of ${\displaystyle \cos \left(45\right)}$ is ${\displaystyle \frac{\sqrt{2}}{2}}$.

The result can be shown in multiple forms.

Exact Form:

Decimal Form: